DNE is what comes at mind first, since lim(x->0-) -sin(x)/2x = -1/2 and lim(x->0+) sin(x)/2x = 1/2 Also, after watching the full video: it is incorrect to use l'hopital to solve this limit, as when applying the derivative definition on sin(x), that same limit (sin(x)/x as x approaches 0) appears, you need to know sin(x)/x ~ 1 (by the squeeze theorem) prior to applying l'hopital
If you check the video that pops up, you’ll see I did a video on just that: using LH rule on the squeeze limit theorem without understanding where it came from is indeed circular. However, with understanding first, it’s more appropriate and even then, the limit in this video is a modification of the famous limit due to the 2 constant and abs sign. So it’s not quite the exact limit that LH rule comes from.
@@NumberNinjaDave sure, the limit is a bit different, but when expanded out into the two other limits they both end up being a k*sin(x)/x limit which again cannot be solved using the LH rule. I'll definitely check out your other vid tho!
You don't HAVE to use L'hopital's rule! Do you see the faster method? Tell me below! Make sure to SUBSCRIBE HERE ⬇ so you don’t miss my tips and tricks for your next exam! tinyurl.com/numberninjadave Gear Up for the Dojo! 🥋 Before you enter the Number Ninja Dojo, you gotta look the part! Grab some awesome Number Ninja swag and show your dedication to mastering math. Shop the collection here: tinyurl.com/numberninjaswag (Affiliate Links Below - As an Amazon Associate I earn from qualifying purchases.) Level Up Your Math Skills with These Must-Haves: 📚 * Conquer Exam Anxiety! 😫➡😌 My book, “Hey Anxiety, Thank You!” is packed with proven strategies to help you master calculus, banish test-day jitters, and ace your exams by first taking care of YOU. Get your copy here: amzn.to/3Y2LWKv * Crush the AP Calculus Exam! 💥 This comprehensive study guide will equip you with the knowledge and practice you need to dominate the AP Calculus exam like a true ninja. Get yours here: amzn.to/3N5pjPm * The Ultimate Calculus Companion: 🧮 This graphing calculator was my trusty sidekick throughout college. It handles complex calculations with ease and never let me down. Get yours here: amzn.to/4eBNeRS * Precision Engineering: 📏 For precise measurements in engineering and other technical fields, this ruler is a must-have. It's durable, accurate, and built to last. Grab yours here: amzn.to/4doupRk Behind the Scenes: My UA-cam Toolkit 🛠 I use VidIQ to help create the best possible UA-cam videos for you! VidIQ helps me optimize my videos, research keywords, and understand what viewers are looking for. If you're a content creator, I highly recommend checking it out. You can sign up here (and I’ll get a small commission if you do): vidiq.com/numberninjadave
sin(x) for small enough x is roughly equal to x. So you could rewrite the problem as lim x->0 of |x|/2x. Split it up because of the bitwise like you did: for x>0 you have lim x->0+ of x/2x and for x0- of -x/2x. Since it's inside a limit, you should be able to dvide the numerator and denominator by x without running into division by 0 problems. This will get you 1/2 and -1/2. I don't think it is that much faster than L'hopital's rule, but I expect this is the method you had in mind.
You can take the 2 in the denominator out of the limit as 1/2 in the positive case, and as -1/2 in the negative case, leaving just sin(x)/x in the limit which is known to equal 1.
DNE is what comes at mind first, since lim(x->0-) -sin(x)/2x = -1/2 and lim(x->0+) sin(x)/2x = 1/2
Also, after watching the full video: it is incorrect to use l'hopital to solve this limit, as when applying the derivative definition on sin(x), that same limit (sin(x)/x as x approaches 0) appears, you need to know sin(x)/x ~ 1 (by the squeeze theorem) prior to applying l'hopital
If you check the video that pops up, you’ll see I did a video on just that: using LH rule on the squeeze limit theorem without understanding where it came from is indeed circular.
However, with understanding first, it’s more appropriate and even then, the limit in this video is a modification of the famous limit due to the 2 constant and abs sign. So it’s not quite the exact limit that LH rule comes from.
@@NumberNinjaDave sure, the limit is a bit different, but when expanded out into the two other limits they both end up being a k*sin(x)/x limit which again cannot be solved using the LH rule. I'll definitely check out your other vid tho!
@@Emdicpau curious what you think of that video of mine!
ua-cam.com/video/uEVCKqQBz3w/v-deo.html
The video cuts off earl
Hahaha well played with missing the y 🥷🧠
lim(sin(x)/2x) =lim(sin(x))1/2x
=1/2lim(sin(x)/x)
=1/2 x 1
=1/2
You forgot the absolute value. Also you appear to lose the 1/x term. Finally the limit of sin x as x approaches 0 is 0, not 1.
@akin0m oh I forgot the /x on the sin your right thanks
And then juste do the same thing for lim(-sin(x)/2x) no ?
You can’t just drop the absolute value without proper analysis.
You don't HAVE to use L'hopital's rule! Do you see the faster method? Tell me below!
Make sure to SUBSCRIBE HERE ⬇ so you don’t miss my tips and tricks for your next exam!
tinyurl.com/numberninjadave
Gear Up for the Dojo! 🥋 Before you enter the Number Ninja Dojo, you gotta look the part! Grab some awesome Number Ninja swag and show your dedication to mastering math. Shop the collection here: tinyurl.com/numberninjaswag
(Affiliate Links Below - As an Amazon Associate I earn from qualifying purchases.)
Level Up Your Math Skills with These Must-Haves: 📚
* Conquer Exam Anxiety! 😫➡😌 My book, “Hey Anxiety, Thank You!” is packed with proven strategies to help you master calculus, banish test-day jitters, and ace your exams by first taking care of YOU. Get your copy here: amzn.to/3Y2LWKv
* Crush the AP Calculus Exam! 💥 This comprehensive study guide will equip you with the knowledge and practice you need to dominate the AP Calculus exam like a true ninja. Get yours here: amzn.to/3N5pjPm
* The Ultimate Calculus Companion: 🧮 This graphing calculator was my trusty sidekick throughout college. It handles complex calculations with ease and never let me down. Get yours here: amzn.to/4eBNeRS
* Precision Engineering: 📏 For precise measurements in engineering and other technical fields, this ruler is a must-have. It's durable, accurate, and built to last. Grab yours here: amzn.to/4doupRk
Behind the Scenes: My UA-cam Toolkit 🛠
I use VidIQ to help create the best possible UA-cam videos for you! VidIQ helps me optimize my videos, research keywords, and understand what viewers are looking for. If you're a content creator, I highly recommend checking it out. You can sign up here (and I’ll get a small commission if you do): vidiq.com/numberninjadave
sin(x) for small enough x is roughly equal to x. So you could rewrite the problem as lim x->0 of |x|/2x. Split it up because of the bitwise like you did: for x>0 you have lim x->0+ of x/2x and for x0- of -x/2x. Since it's inside a limit, you should be able to dvide the numerator and denominator by x without running into division by 0 problems. This will get you 1/2 and -1/2.
I don't think it is that much faster than L'hopital's rule, but I expect this is the method you had in mind.
You can take the 2 in the denominator out of the limit as 1/2 in the positive case, and as -1/2 in the negative case, leaving just sin(x)/x in the limit which is known to equal 1.
@@twinkskeptic9029 nicely done, ninja!