Here is a difficult limit with a rational number solution. limit (2x^3 + 4/√x - 130 ) / (x - 4) , as x → 4 . The answer is 383/4. See if you can find a way to show that, without using Lhopitals rule.
...Good day to you, I have always found the "LImits" part of mathematics (calculus) interesting, because this part regularly demands the utmost of your math (algebra) skills, not to mention creativity. Being rather inquisitive by nature, I always try to look for more solution methods, than just following the well-known familiar strategies. The same goes for your demonstrated limit: lim(x-->3)((sqrt(2x-5) - 1)/(x - 3)). First I try to investigate whether I can rewrite the denominator x - 3 in the form of (2x - 5) - 1 in some kind of way, and then consider this new denominator as a difference of squares, so: x - 3 = (2x - 5) - 1 = (sqrt(2x-5) - 1)(sqrt(2x-5) + 1), and finally cancel any common factors in numerator and denominator. My solution path for your limit now follows: lim(x-->3)((sqrt(2x-5) - 1)/(x - 3)) = lim(x-->3)((2/2)(sqrt(2x-5) - 1)/(x - 3)) = (2)lim(x-->3)((sqrt(2x-5) - 1)/(2(x - 3)) = (2)lim(x-->3)((sqrt(2x-5) - 1)/((2x - 5) - 1)) = (2)lim(x-->3)((sqrt(2x-5) - 1)/((sqrt(2x-5) - 1)(sqrt(2x-5) + 1)) = (2)lim(x-->3)(1/(sqrt(2x-5) + 1)) = (2)(1/2) = 1. So I had to start multiplying the numerator and denominator both by 2, to be able to create the new denominator: 2(x - 3) = 2x - 6 = (2x - 5) -1. I have placed the factor 2 of the numerator outside the limit in accordance with the rules for limits. And finally we get the same result for your limit, namely 1. I hope you liked this alternative way of solving your given limit... Thanking you for your mathematics efforts, Jan-W
@@jaysonbalanday6054 There is no simple formula. It's better to watch the video and use the process than to follow a pre-constructed formula that sometimes work.
thanks for saving me
This caption is mad
Here is a difficult limit with a rational number solution.
limit (2x^3 + 4/√x - 130 ) / (x - 4) , as x → 4 .
The answer is 383/4. See if you can find a way to show that, without using Lhopitals rule.
That's a good one!
Thanks for the help
...Good day to you, I have always found the "LImits" part of mathematics (calculus) interesting, because this part regularly demands the utmost of your math (algebra) skills, not to mention creativity. Being rather inquisitive by nature, I always try to look for more solution methods, than just following the well-known familiar strategies. The same goes for your demonstrated limit: lim(x-->3)((sqrt(2x-5) - 1)/(x - 3)). First I try to investigate whether I can rewrite the denominator x - 3 in the form of (2x - 5) - 1 in some kind of way, and then consider this new denominator as a difference of squares, so: x - 3 = (2x - 5) - 1 = (sqrt(2x-5) - 1)(sqrt(2x-5) + 1), and finally cancel any common factors in numerator and denominator. My solution path for your limit now follows: lim(x-->3)((sqrt(2x-5) - 1)/(x - 3)) = lim(x-->3)((2/2)(sqrt(2x-5) - 1)/(x - 3)) = (2)lim(x-->3)((sqrt(2x-5) - 1)/(2(x - 3)) = (2)lim(x-->3)((sqrt(2x-5) - 1)/((2x - 5) - 1)) = (2)lim(x-->3)((sqrt(2x-5) - 1)/((sqrt(2x-5) - 1)(sqrt(2x-5) + 1)) = (2)lim(x-->3)(1/(sqrt(2x-5) + 1)) = (2)(1/2) = 1. So I had to start multiplying the numerator and denominator both by 2, to be able to create the new denominator: 2(x - 3) = 2x - 6 = (2x - 5) -1. I have placed the factor 2 of the numerator outside the limit in accordance with the rules for limits. And finally we get the same result for your limit, namely 1. I hope you liked this alternative way of solving your given limit... Thanking you for your mathematics efforts, Jan-W
I have a formula in this lesson that it takes 3 to 5 seconds to solve.
how
@@deliveringIdeas i can share it with you if you want.
@@jaysonbalanday6054 Please tell me.
@@deliveringIdeas in what way?
@@jaysonbalanday6054 There is no simple formula. It's better to watch the video and use the process than to follow a pre-constructed formula that sometimes work.