Embibe Experts Solutions for Chapter: Limits, Exercise 1: JKCET 2018

The value of $\underset{x\to 2}{\lim }\frac{\sqrt{1+\sqrt{2+x}}-\sqrt{3}}{x-2}$ is

If $f\left(x\right)=\frac{2}{x-3},g\left(x\right)=\frac{x-3}{x+4}$ and $h\left(x\right)=-\frac{2(2x+1)}{x^2+x-12}$, then $\underset{x\to 3}{\lim }\left[f\right(x)+g(x)+h(x\left)\right]$ is

The value of $\underset{x\to 0}{\lim }\left\{\frac{\sin x-x}{x^3}\right\}$ equals to

If $n>0$, then the value of $\underset{x\to \infty }{\lim }\frac{\log x}{x^n}$ is

What are the values of constants ' $a$ ' and ' $b$ ', so that $\underset{x\to \infty }{\lim }\left(\frac{x^2+1}{x+1}-ax-b\right)=0?$

The value of $\underset{x\to \infty }{\lim }{\left(\frac{x^2+2x+3}{2x^2+x+5}\right)}^{\frac{3x-2}{3x+2}}$ is

It is given that $f\left(x\right)=\frac{-3\mathrm{x}+(-1{)}^x}{4\mathrm{x}-(-1{)}^x}$ The limit value of the function $f\left(x\right)$ as $x$ tends to infinity is