Question

Please explain how to evaluate the limit. I have the answer, but don't know the why. Limit at x approaches 0 from the left of (sin(-5x))/(8x). The answer is -5/8

Answer 1

If you use l'hopital's rule then it would be very easy ~ taking the derivative of the top and the derivative of the bottom separately and then recombine them together. You would get
[d/dx (sin(-5x))] / [d/dx (8x)] = -5cos(-5x)/8 and if you take the limit as x approaches zero then you would get -5/8

Answer 2

I'm somewhat familiar with l'hospitals rule, this problem comes before that in the unit. Do you know how to explain the long way?

Answer 3

I don't remember all of the different ways to solve these equations no, however do you have a book that shows an example of solving something like this?

Answer 4

I'm working on mooculus to review. This is part of a larger problem. I'll try to post the context.

Answer 5

http://www.analyzemath.com/calculus/limits/squeezing.html
This might help, but I really don't know, I can't find anything other than "squeezing theorem" (which I don't remember really how it works) and l'hopital's rule, =/ I'm sorry.

Answer 6

I'll check it out, thank you. Do you know if I can post pictures here. I'm on an iPad and I took a screen shot of the problem.