Integration Bee Training for Advanced #16.6 - Tricky Limit Substitutions

Memorable Timestamps:
0:15 - A Common Substitution Example
2:33 - A Tricky Limit Casework
15:31 - Another Nice Example
17:32 - Substitute by Bounds
21:16 - A Cool Gaussian Limit
24:53 - An MIT Style Limit Integral
28:23 - A Harder Version
32:33 - Another Another Nice Example
34:15 - An Awkward Looking Limit Integral
38:12 - An Intimidating Example
42:34 - Forced Limit Substitution
45:20 - It doesn't always have to cancel out

[@phat5340]

The last one is a great example to use the weisstrass theorem, since if you had a power of x instead of e^x you would have gotten 2 and you know that e^x = sum x^n/n! so the int would be 2 * sum 1/n! = 2e

[@qwertyman123]

this guy is cooking

[@jaspercarran3432]

🐐

[@Titanic_shirohige]

could we have substituted nx = u and then taken the limit, the answer comes out the same
in the second one

[@Silver-cu5up]

I dont think so becuz of the bounds? If I do that limit sub ill get from 0 to inf.

[@Titanic_shirohige]

drive.google.com/file/d/1YFUw1nfVpml5Jd_PaoiWDRRoJ7GfPzGc/view?usp=drivesdk

[@Titanic_shirohige]

Could you tell which step wa wrong

[@Silver-cu5up]

@@Titanic_shirohige letting u=nx is wrong

[@evankniffen]

go to sleep brother goodness gracious

[@Silver-cu5up]

Ill be okeh hehehe @_@