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

Evaluate $\underset{x\to 1}{\mathrm{Lim}}\frac{\left[{\sum }_{k=1}^{100}{x}^k\right]-100}{x-1}$

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

If $\underset{x\to 0}{\lim }\frac{ax-\left(e^{4x}-1\right)}{ax\left(e^{4x}-1\right)}$ exists and is equal to $b$, then the value of $a-2b$ is ___ .

What is the value of $\underset{x\to \infty }{\lim }{\left(\frac{x+6}{x+1}\right)}^{x+4}$ ?

If $f\left(9\right)=9$ and $f^{\text{'}}\left(9\right)=4$, then what is $\underset{x\to 9}{\lim }\frac{\sqrt{f\left(x\right)}-3}{\sqrt{x}-3}$ equal to?

What is $\underset{x\to 0}{\lim }\frac{{\left(1+x\right)}^n-1}{x}$ 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 $\underset{x\to 0}{\lim }\left\{\frac{x\left(1+a\cos x\right)-b\sin x}{x^3}\right\}=1$, then