Thursday, August 17, 2017

calculus - Are all limits solvable without L'Hôpital Rule or Series Expansion

Is it always possible to find the limit of a function without using L'Hôpital Rule or Series Expansion?




For example,



$$\lim_{x\to0}\frac{\tan x-x}{x^3}$$



$$\lim_{x\to0}\frac{\sin x-x}{x^3}$$



$$\lim_{x\to0}\frac{\ln(1+x)-x}{x^2}$$



$$\lim_{x\to0}\frac{e^x-x-1}{x^2}$$




$$\lim_{x\to0}\frac{\sin^{-1}x-x}{x^3}$$



$$\lim_{x\to0}\frac{\tan^{-1}x-x}{x^3}$$

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...