Embibe Experts Solutions for Chapter: Limits, Exercise 1: Exercise 1

What is $\underset{x\to 0}{\lim }\frac{{\log }_5\left(1+x\right)}{x}$ equal to?

What is $\underset{x\to 0}{\lim }{e}^{-\frac{1}{x^2}}$ equal to?

What is $\underset{x\to 0}{\lim }\frac{{\left(1+x\right)}^n-1}{x}$ equal to?

What is $\underset{x\to 0}{\lim }\frac{5^x-1}{x}$ equal to?

What is $\underset{n\to \infty }{\lim }\frac{1+2+3+\dots +n}{1^2+2^2+3^2+\dots +n^2}$ equal to?

If $f\left(x\right)=\sqrt{25-x^2},$ then what is $\underset{x\to 1}{\lim }\frac{f\left(x\right)-f\left(1\right)}{x-1}$ equal to?

If $f\left(x\right)=\frac{\sin \left(e^{x-2}-1\right)}{\ln \left(x-1\right)}$, then $\underset{x\to 2}{\lim }f\left(x\right)$ is equal to

If $\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sin x}{x}=l$ and $\underset{x\to \infty }{\lim }\frac{\cos x}{x}=m$, then which one of the following is correct $?$