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Laurent Series Expansions Explained with Example Questions
Questions which directly ask Laurent Series expansions are not that common, but they do come up occasionally - as such it is well worth getting to grips with them. In this video we examine three questions which ask for Laurent Series expansions about five regions, giving a good overview of the questions one might expect and how to deal with them.
Important Note: At 20:38 the author incorrectly writes "2(n+1)" instead of "2n+3".
For more videos on Taylor and Laurent series see our playlist 'Taylor, Maclaurin and Laurent Series' at ua-cam.com/play/PLlX3COjsHPVDtqWHOePVICdolA2hw6gvl.html
Переглядів: 283

Відео

A Familiar Looking Integral made Much Harder with Complex Coefficients13:42A Familiar Looking Integral made Much Harder with Complex Coefficients
A Familiar Looking Integral made Much Harder with Complex Coefficients
Переглядів 8457 годин тому
In this video we tackle a familiar looking integral, but made much more difficult because we are dealing with complex variables and complex coefficients rather than their real counterparts. The method to solve is similar to that with real variables and coefficients, but every step (except bizarrely the final integral) is more difficult. Having said that, with care not to make mistakes, the inte...
Quick Method to Find Interval of Convergence of Taylor Series Expansion of a/(bx+c) about a Point13:02Quick Method to Find Interval of Convergence of Taylor Series Expansion of a/(bx+c) about a Point
Quick Method to Find Interval of Convergence of Taylor Series Expansion of a/(bx+c) about a Point
Переглядів 84812 годин тому
In a time constrained situation such as an exam, any seconds gained are valuable and the method explained in this video allows the solving of the question on the thumbnail in a few seconds (as opposed to a few minutes by more traditional methods). First we show the method, then we show the more traditional method (Taylor series expansion and the ratio test) and finally we explain why the quick ...
Two Correct (and One Incorrect) Methods to Find this Limit7:35Two Correct (and One Incorrect) Methods to Find this Limit
Two Correct (and One Incorrect) Methods to Find this Limit
Переглядів 1,2 тис.16 годин тому
This is a very common limit question which can be answered in a relatively straightforward manner using Taylor expansion or L'Hopital - however there is a third (incorrect) way which some students attempt, which involves adding and subtracting infinity (which clearly cannot be done) For more videos on limits see our playlist 'Limits' ua-cam.com/play/PLlX3COjsHPVDc_qtVRdkPjEmNVMx2abvo.html For m...
Taylor Series Expansions and Approximations12:55Taylor Series Expansions and Approximations
Taylor Series Expansions and Approximations
Переглядів 86521 годину тому
The two questions that we discuss in this video are a very common question type on Senior High School Maths exams and College Entrance exams, and with care it is one where gaining maximum marks is not beyond the average student. As such, it is well worth getting to grips with the techniques discussed. The questions follow a typical pattern being a) find the Taylor Expansion of a function about ...
Maclaurin Series Expansions and Partial Fractions13:16Maclaurin Series Expansions and Partial Fractions
Maclaurin Series Expansions and Partial Fractions
Переглядів 716День тому
This is a very common question on Senior High School Maths exams and College Entrance exams, and with care it is one where gaining maximum marks is not beyond the average student. As such, it is well worth getting to grips with the techniques discussed in this video. For more videos on Maclaurin/ Taylor series see our playlist 'Taylor, Maclaurin and Laurent Series' at ua-cam.com/play/PLlX3COjsH...
L'Hopital Trap for the Unwary4:27L'Hopital Trap for the Unwary
L'Hopital Trap for the Unwary
Переглядів 2,9 тис.14 днів тому
L'Hopital Trap for the Unwary
Partial and Total Differentiation and Independent and Dependent Variables8:26Partial and Total Differentiation and Independent and Dependent Variables
Partial and Total Differentiation and Independent and Dependent Variables
Переглядів 1 тис.14 днів тому
Partial and Total Differentiation and Independent and Dependent Variables
Implicit Partial Differentiation and Independent Variables13:39Implicit Partial Differentiation and Independent Variables
Implicit Partial Differentiation and Independent Variables
Переглядів 78514 днів тому
Implicit Partial Differentiation and Independent Variables
Partial Differentiation but Keeping which Variables Constant?11:07Partial Differentiation but Keeping which Variables Constant?
Partial Differentiation but Keeping which Variables Constant?
Переглядів 1,7 тис.21 день тому
Partial Differentiation but Keeping which Variables Constant?
Premises, Conclusions and Valid or Invalid Arguments8:04Premises, Conclusions and Valid or Invalid Arguments
Premises, Conclusions and Valid or Invalid Arguments
Переглядів 1,1 тис.21 день тому
Premises, Conclusions and Valid or Invalid Arguments
Volume of Integration and Rate of Change Question - Great GRE Subject Maths Revision Practice7:53Volume of Integration and Rate of Change Question - Great GRE Subject Maths Revision Practice
Volume of Integration and Rate of Change Question - Great GRE Subject Maths Revision Practice
Переглядів 69028 днів тому
Volume of Integration and Rate of Change Question - Great GRE Subject Maths Revision Practice
Connecting Definite Integrals, Limits to Infinity of Sums and Riemann Sums17:08Connecting Definite Integrals, Limits to Infinity of Sums and Riemann Sums
Connecting Definite Integrals, Limits to Infinity of Sums and Riemann Sums
Переглядів 1 тис.Місяць тому
Connecting Definite Integrals, Limits to Infinity of Sums and Riemann Sums
Avoiding Extraneous Solutions with the Lambert W Function3:39Avoiding Extraneous Solutions with the Lambert W Function
Avoiding Extraneous Solutions with the Lambert W Function
Переглядів 1,4 тис.Місяць тому
Avoiding Extraneous Solutions with the Lambert W Function
Finding ALL Solutions with the Lambert W Function6:39Finding ALL Solutions with the Lambert W Function
Finding ALL Solutions with the Lambert W Function
Переглядів 939Місяць тому
Finding ALL Solutions with the Lambert W Function
How to Solve an Exponential Equation with the Lambert W Function8:13How to Solve an Exponential Equation with the Lambert W Function
How to Solve an Exponential Equation with the Lambert W Function
Переглядів 433Місяць тому
How to Solve an Exponential Equation with the Lambert W Function
Reconciling Two Seemingly Completely Different Lambert W Solutions9:02Reconciling Two Seemingly Completely Different Lambert W Solutions
Reconciling Two Seemingly Completely Different Lambert W Solutions
Переглядів 6962 місяці тому
Reconciling Two Seemingly Completely Different Lambert W Solutions
Solving Coin Toss Problems with Markov Chains13:28Solving Coin Toss Problems with Markov Chains
Solving Coin Toss Problems with Markov Chains
Переглядів 1,3 тис.2 місяці тому
Solving Coin Toss Problems with Markov Chains
GMAT / GRE 'Work' Word Problem with a Twist6:34GMAT / GRE 'Work' Word Problem with a Twist
GMAT / GRE 'Work' Word Problem with a Twist
Переглядів 1243 місяці тому
GMAT / GRE 'Work' Word Problem with a Twist
Complex Line Integrals and the Fundamental Theorem of Calculus14:53Complex Line Integrals and the Fundamental Theorem of Calculus
Complex Line Integrals and the Fundamental Theorem of Calculus
Переглядів 1433 місяці тому
Complex Line Integrals and the Fundamental Theorem of Calculus
Integrating Complex Valued Functions of a Real Variable12:45Integrating Complex Valued Functions of a Real Variable
Integrating Complex Valued Functions of a Real Variable
Переглядів 3073 місяці тому
Integrating Complex Valued Functions of a Real Variable
Finding the Harmonic Conjugates of a Complex Differentiable Function6:55Finding the Harmonic Conjugates of a Complex Differentiable Function
Finding the Harmonic Conjugates of a Complex Differentiable Function
Переглядів 2263 місяці тому
Finding the Harmonic Conjugates of a Complex Differentiable Function
Three Questions on Complex Differentiation and the Cauchy-Riemann Equations8:57Three Questions on Complex Differentiation and the Cauchy-Riemann Equations
Three Questions on Complex Differentiation and the Cauchy-Riemann Equations
Переглядів 2323 місяці тому
Three Questions on Complex Differentiation and the Cauchy-Riemann Equations
Differentiating Trigonometric Identities Cos z and Sin z for Complex z11:18Differentiating Trigonometric Identities Cos z and Sin z for Complex z
Differentiating Trigonometric Identities Cos z and Sin z for Complex z
Переглядів 2623 місяці тому
Differentiating Trigonometric Identities Cos z and Sin z for Complex z
Investigating Trigonometric Identities with Complex Numbers10:43Investigating Trigonometric Identities with Complex Numbers
Investigating Trigonometric Identities with Complex Numbers
Переглядів 1343 місяці тому
Investigating Trigonometric Identities with Complex Numbers
Understanding Complex Solutions of sin (θ) = a10:23Understanding Complex Solutions of sin (θ) = a
Understanding Complex Solutions of sin (θ) = a
Переглядів 2533 місяці тому
Understanding Complex Solutions of sin (θ) = a
Understanding Complex Solutions of cos (θ) = a12:36Understanding Complex Solutions of cos (θ) = a
Understanding Complex Solutions of cos (θ) = a
Переглядів 3064 місяці тому
Understanding Complex Solutions of cos (θ) = a
Finding all Real and Complex Solutions of a Trigonometric Equation9:28Finding all Real and Complex Solutions of a Trigonometric Equation
Finding all Real and Complex Solutions of a Trigonometric Equation
Переглядів 2714 місяці тому
Finding all Real and Complex Solutions of a Trigonometric Equation
Absorbing Markov Chains Solved with Transition and Solution Matrices22:10Absorbing Markov Chains Solved with Transition and Solution Matrices
Absorbing Markov Chains Solved with Transition and Solution Matrices
Переглядів 1894 місяці тому
Absorbing Markov Chains Solved with Transition and Solution Matrices
Absorbing Markov Chains, Total Probabilities and Recursion16:18Absorbing Markov Chains, Total Probabilities and Recursion
Absorbing Markov Chains, Total Probabilities and Recursion
Переглядів 3084 місяці тому
Absorbing Markov Chains, Total Probabilities and Recursion

КОМЕНТАРІ

  • @grestyacademy
    @grestyacademy 5 годин тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy День тому

    For more videos on Laurent and Taylor Series expansions see our playlist 'Taylor, Maclaurin and Laurent Series' at ua-cam.com/play/PLlX3COjsHPVDtqWHOePVICdolA2hw6gvl.html

  • @grestyacademy
    @grestyacademy 2 дні тому

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  • @grestyacademy
    @grestyacademy 3 дні тому

    For more videos on complex numbers, check out our playlist 'Complex Numbers' at ua-cam.com/play/PLlX3COjsHPVC9MnNSwdVOfFk6zALYYEAm.html

  • @grestyacademy
    @grestyacademy 4 дні тому

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  • @Killerjay_38927
    @Killerjay_38927 4 дні тому

    Broo you can solve it by 1st method i think where you wrote infinity + infinity + infinity but um getting ans 2 by that

  • @grestyacademy
    @grestyacademy 5 днів тому

    For more videos on Taylor Series expansions see our playlist 'Taylor, Maclaurin and Laurent Series' at ua-cam.com/play/PLlX3COjsHPVDtqWHOePVICdolA2hw6gvl.html

  • @m416gurujigaming9
    @m416gurujigaming9 5 днів тому

    why no comment?

    • @grestyacademy
      @grestyacademy 5 днів тому

      Good question - alas not one to which I have an answer!🤔

  • @grestyacademy
    @grestyacademy 6 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

    • @rajkotalovic9784
      @rajkotalovic9784 5 днів тому

      Uopste ne razumem pitanje ni sta ono znaci, gde se ovo upotrebljava?

    • @grestyacademy
      @grestyacademy 5 днів тому

      Well for example the first term 4^(3^2) just means raise 4 to the power of 3^2 (which is 9) - ie 4x4x4x4x4x4x4x4x4 etc - its a teaser testing knowledge of exponent rules - hope this helps

  • @grestyacademy
    @grestyacademy 7 днів тому

    For more videos on Maclaurin Series expansions see our playlist 'Taylor, Maclaurin and Laurent Series' at ua-cam.com/play/PLlX3COjsHPVDtqWHOePVICdolA2hw6gvl.html

  • @grestyacademy
    @grestyacademy 8 днів тому

    For more on the Fundamental Theorem of Calculus see our video 'How to Answer Fundamental Theorem of Calculus Exam Questions' at ua-cam.com/video/n-_9LQQKMno/v-deo.html

  • @grestyacademy
    @grestyacademy 8 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy 9 днів тому

    For more videos on Taylor Series expansions see our playlist 'Taylor, Maclaurin and Laurent Series' at ua-cam.com/play/PLlX3COjsHPVDtqWHOePVICdolA2hw6gvl.html

  • @grestyacademy
    @grestyacademy 10 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy 11 днів тому

    For more videos on Maclaurin Series expansions see our playlist 'Taylor, Maclaurin and Laurent Series' at ua-cam.com/play/PLlX3COjsHPVDtqWHOePVICdolA2hw6gvl.html

  • @PawełDąbrowski-n3w
    @PawełDąbrowski-n3w 11 днів тому

    How to solve it with more "pure mathematical" methods?

    • @grestyacademy
      @grestyacademy 11 днів тому

      Great question - there is a way to solve mathematically using addition mod 90 (with adjustments) and then subtraction mod 9 (with adjustments) - but it is a bit ugly. Of course if the number wheel had a zero as well then mod 100 and mod 10 would make a quite neat formula.

  • @grestyacademy
    @grestyacademy 12 днів тому

    For those desirous of a clue 'Think Number Wheel'. For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @WizardPower_
    @WizardPower_ 12 днів тому

    This can all be resolved by substituting sin x for x and you get lim x-> inf of 1/x^2 which is infinity

    • @grestyacademy
      @grestyacademy 12 днів тому

      yes - but the 'go to' method for most people is L'Hopital (for good reason as it often gets the correct limit quickly) - but it has to be applied correctly (ie indeterminate at every step where it is used).

  • @mreathaoof588
    @mreathaoof588 13 днів тому

    Another way you could do it, I believe, is by changing it into the form "(1/x^2)*(sin(x)/x)". If we were to take the limit as x approaches 0, we would get (1/0^2)*1 (because of the lim x->0 sin(x)/x=1), which is another way to get the answer of infinity.

    • @grestyacademy
      @grestyacademy 13 днів тому

      Yes agree (I presume you meant to type 'because of the lim x->0 sin(x)/x=1')

    • @mreathaoof588
      @mreathaoof588 13 днів тому

      @@grestyacademyYes, I did mean to write =1, thanks for catching that mistake

  • @grestyacademy
    @grestyacademy 13 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  •  13 днів тому

    you could reach the same result by observing that 1/0 approaches +infinity after initially applying l'hopital's rule. in this particular case, there's no need to use Taylor expansions.

    • @grestyacademy
      @grestyacademy 13 днів тому

      Correct and good point, thanks for sharing. Though the main point of the video is that it is an easy trap to fall into NOT checking whether the expression is still indeterminate and therefore eligible for l'Hopital at EVERY step of the calculation. Many students just check the expression is indeterminate at step one and therefore assume L'Hopital can be applied at all steps until there is a limit which can be evaluated.

  • @pedroivog.s.6870
    @pedroivog.s.6870 13 днів тому

    So you can't just apply L'Hospital everywhere 😢 /j

    • @grestyacademy
      @grestyacademy 13 днів тому

      Alas not - only on indeterminate forms such as 0/0 etc

  • @grestyacademy
    @grestyacademy 14 днів тому

    For those desirous of a clue 'Think Maths meets English'. For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @siddharthjp8497
    @siddharthjp8497 14 днів тому

    These set of questions will fetch a lot of marks in jee. Students preparing for competive exams must watch these videos to attempt distribution questions.

    • @grestyacademy
      @grestyacademy 14 днів тому

      Agree completely and thanks for the support - hence we have compiled a playlist entitled 'Counting Identical/Distinct Objects' at ua-cam.com/play/PLlX3COjsHPVCFZNiawIWvdC_kj56USiEc.html where we have videos explaining the various types of 'identical/distinct' objects/containers questions that are encountered!

  • @iwonder2218
    @iwonder2218 14 днів тому

    You incorrectly applied l'hospitals the second time because the expression was 1/0 at that point. This accounts for the discrepancy in your results.

    • @grestyacademy
      @grestyacademy 14 днів тому

      Correct - as I say in the video at 3:20

    • @almightysapling
      @almightysapling 12 днів тому

      Okay but I didn't even get to 3:20 cuz I looked at the thumbnail and said "no, Lhopitals does not get you -1/6 it gets you infinity". It's not an issue of approach.

    • @grestyacademy
      @grestyacademy 12 днів тому

      agree - but it's a trap a lot of people fall into (clearly not you)...hence the video to remind students they must check the form is still indeterminate at every step and not just focus on the x^3 on the bottom and immediately apply L'Hopital three times because it can be applied at step one

  • @grestyacademy
    @grestyacademy 15 днів тому

    For more videos on limits see our playlist 'Limits' at ua-cam.com/play/PLlX3COjsHPVDc_qtVRdkPjEmNVMx2abvo.html

  • @conchoprimo
    @conchoprimo 15 днів тому

    I don’t understand the result for alice. When you toss both coins at the same time, is that count as two tosses?

    • @grestyacademy
      @grestyacademy 15 днів тому

      yes exactly...because she is tossing two coins (just at the same time). Hope that's clear

  • @grestyacademy
    @grestyacademy 16 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy 17 днів тому

    For more videos on partial differentiation check out our playlist 'Partial Differentiation' at ua-cam.com/play/PLlX3COjsHPVD3ur62I9iCF0sKFerXWXPs.html

  • @grestyacademy
    @grestyacademy 18 днів тому

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  • @muhammedalik1
    @muhammedalik1 18 днів тому

    Great Explaination!🎉 Sir, your way of writing the letter 'z' is strange but its beautifully unique!

    • @grestyacademy
      @grestyacademy 18 днів тому

      Thanks for the feedback and support! As for the 'z' I had never really thought about it, but yes you are right 😎🙃

  • @grestyacademy
    @grestyacademy 19 днів тому

    For more videos on partial differentiation check out our playlist 'Partial Differentiation' at ua-cam.com/play/PLlX3COjsHPVD3ur62I9iCF0sKFerXWXPs.html

  • @grestyacademy
    @grestyacademy 20 днів тому

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  • @grestyacademy
    @grestyacademy 21 день тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy 22 дні тому

    IMPORTANT NOTE: At 5:35 the author misses out a 'y' - it should read v=y+3xy^2 NOT v=y+3x^2 - however all of the maths following it is correct. For more videos on the chain rule see our playlist 'Chain Rule' at ua-cam.com/play/PLlX3COjsHPVBhyHwVmKS7RYCS0SqHULST.html.

  • @grestyacademy
    @grestyacademy 23 дні тому

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  • @grestyacademy
    @grestyacademy 24 дні тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @karan440
    @karan440 24 дні тому

    The clarity you've given me today you sir 've got my respect

    • @grestyacademy
      @grestyacademy 24 дні тому

      Very kind of you to say - thanks for the support! If you are studying this topic you may be interested in our playlist 'Counting Identical/Distinct Distributions' at ua-cam.com/play/PLlX3COjsHPVCFZNiawIWvdC_kj56USiEc.html

  • @grestyacademy
    @grestyacademy 25 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy 26 днів тому

    For more videos on Logic see our playlist 'Logic and Reasoning' at ua-cam.com/play/PLlX3COjsHPVC1-RhCIjX3pPxfQHIdlxP3.html

  • @grestyacademy
    @grestyacademy 27 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy 28 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy 29 днів тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy Місяць тому

    For more videos on GRE Subject Maths, check out out playlist 'GRE Subject Maths' at ua-cam.com/play/PLlX3COjsHPVCpFemZUNEy1tsNK4LlxG-S.html

  • @grestyacademy
    @grestyacademy Місяць тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @mecha37000fighter
    @mecha37000fighter Місяць тому

    Thank you, this was very helpful in understanding the subject🫡

    • @grestyacademy
      @grestyacademy Місяць тому

      Glad to be of service - thanks for the feedback. We have a few Lambert W Function videos up on our channel if you are interested - check out the playlist 'Lambert W Function' at ua-cam.com/play/PLlX3COjsHPVApqLukQcbj2e9rDC5sRg_t.html

  • @grestyacademy
    @grestyacademy Місяць тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @SaliniBabulena-nk7ln
    @SaliniBabulena-nk7ln Місяць тому

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  • @grestyacademy
    @grestyacademy Місяць тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html

  • @grestyacademy
    @grestyacademy Місяць тому

    For more Gresty Academy 'One Minute Teasers' and 'Weekend Workouts' see our playlist 'Miscellaneous Shorts' ua-cam.com/play/PLlX3COjsHPVB9MwWLYpVV5cLbFmBUayZY.html