Embibe Experts Solutions for Chapter: Limits, Exercise 1: WBJEE 2020

Let $0<\alpha <\beta <1$. Then, $\underset{n\to \infty }{\lim }{\int }_{1/(k+\beta )}^{1/(k+\alpha )}\frac{\mathrm{d}x}{1+x}$ is

Let $f\left(x\right)=\frac{1}{3}x\sin x-\left(1-\cos x\right)$. The smallest positive integer $k$ such that $\underset{x\to 0}{\lim }\frac{f\left(x\right)}{x^k}\ne 0$ is

The limit of the interior angle of a regular polygon of $n$ sides as $n\to \infty$ is

If $\underset{x\to 0}{\lim }{\left(\frac{1+cx}{1-cx}\right)}^{1/x}=4,$ then $\underset{x\to 0}{\lim }{\left(\frac{1+2cx}{1-2cx}\right)}^{1/x}$ is

$\underset{x\to 1}{\lim }\left(\frac{1}{\ln x}-\frac{1}{(x-1)}\right)$

$\underset{x\to 0^{+}}{\lim }\left(x^n\ln x\right), n>0$

$\underset{x\to 0^{+}}{\lim }{\left(e^x+x\right)}^{1/x}$

Let $f\left(x\right)=3x^{10}-7x^8+5x^6-21x^3+3x^2-7$. Then, $\underset{h\to 0}{\lim }\frac{f(1-h)-f\left(1\right)}{h^3+3h}$