Embibe Experts Solutions for Chapter: Limits, Exercise 1: TS EAMCET - 5 August 2021 Shift 1

If  $f\left(x\right)=\left\{\begin{array}{cc}\frac{\sin \left[x\right]}{\left[x\right]},& \left[x\right]\ne 0\\ 0,& \left[x\right]=0\end{array},\right.$ where $\left[x\right]$ denotes the greatest integer less than or equal to $x,$ then $\underset{x\to 0^{-}}{\lim }f\left(x\right)$

$\underset{x\to -\infty }{\lim }\frac{3|x{|}^3-x^2+2|x|-5}{-5|x{|}^3+3x^2-2|x|+7}=$

If $f\left(x\right)=x^2\sin \frac{1}{x},$ when $x\ne 0$ and $f\left(0\right)=0,$ then $\underset{x\to 0}{\lim }{f}^{\text{'}}\left(x\right)$

$\underset{x\to 0}{\lim }\frac{\left(1-\cos 2x\right)}{x\tan 2x+\frac{2x}{3}\tan 3x}=$

$\underset{x\to 0}{\lim }\frac{x^2{2}^x-x^2\sin x-x^2}{3^x+\cos x-3^x\cos x-1}=$

If $\underset{x\to 2}{\lim }\frac{3x^2-ax+5b}{x-2}=17$, then $ab=$

If $f\left(x\right)={\tan }^{-1}\left(\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right)$, then $\underset{{}_{x\to \frac{1}{2}}}{\lim }\frac{2\left[f\left(x\right)-f\left(\frac{1}{2}\right)\right]}{2x-1}=$

$\underset{n\to \infty }{\lim }P{\left(1+\frac{r}{100n}\right)}^{tn}=$