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

$\underset{x\to 0}{\lim }\left(\frac{{\log }_e\cos x}{x^2}\right)$ is equal to

$\underset{x\to 0}{\lim }\left(\frac{{10}^x-2^x-5^x+1}{x\tan x}\right)$ is equal to

$\underset{x\to \infty }{\lim }{\left(\frac{2x^2+3}{2x^2+5}\right)}^{8x^2+3}$ is equal to

$\underset{x\to 0}{\lim }{\left(\frac{3}{1+\sqrt{4+x}}\right)}^{\mathrm{cosec}x}$ has the value equal to

The value of $\underset{x\to 0}{\lim }{\left(\cos ax\right)}^{{\mathrm{cosec}}^{2}bx}$ is

Let $r=\underset{x\to 0}{\lim }{\left(\frac{\sin x}{x}\right)}^{\frac{1}{x}}$ and $m=\underset{x\to 0}{\lim }{\left(\frac{\sin x}{x}\right)}^{\frac{1}{x^2}}$, then

$\underset{x\to 0}{\lim }\left(\frac{\sqrt[3]{1+3x}-1-x}{{\left(1+x\right)}^{101}-1-101x}\right)$ has the value equal to-

$\underset{x\to 0}{\lim }\left(\frac{e^{x^3}-\tan x+\sin x-1}{x^n}\right)$ exists and is non-zero, then the value of $n$ is