Evaluate the following one sided limits: _ x 2^- x-3 x^2-4 . - Vidyadip

Question

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow2^-}\frac{\text{x}-3}{\text{x}^2-4}.$

✓

Answer

$\lim\limits_{\text{x}\rightarrow2^-}\frac{\text{x}-3}{(\text{x}^2-4)}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{(2-\text{h})-3}{(2-\text{h)}^2-4^2}$ $\Big[\because\lim\limits_{\text{x}\rightarrow2^-}\text{f(x)}=\lim\limits_{\text{h}\rightarrow0}\text{f}(2-\text{h)}\Big]$
$=\lim\limits_{\text{h}\rightarrow0}\frac{(2-\text{h}-3)}{(2-\text{h}+2)(2-\text{h}-2)}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{-1-\text{h}}{(4-\text{h})(-\text{h})}$
$=\lim\limits_{\text{h}\rightarrow0}\frac{\frac{1}{\text{h}}+1}{(4-\text{h})}$
$=\frac{\frac{1}{0}+1}{4}=\infty$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Limits→Limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the middle term in the expansion of:
$\Big(3{\text{x}}-\frac{2}{\text{x}^2}\Big)^{15}$

How many $3-$digit even number can be made using the digits $1, 2, 3, 4, 5, 6, 7,$ if no digits is repeated?

Find the coefficient of:
$x^{-15}$ in the expansion of $\Big(3\text{x}^2-\frac{\text{a}}{3\text{x}^3}\Big)^{10}.$

Find the sum of the terms of an infinite decreasing G.P. in which all the terms are positive, the first term is 4, and the difference between the third and fifth term is equal to $\frac{32}{81}.$

If $\sin\text{A}=\frac{1}{2},$ $\cos\text{B}=\frac{12}{13},$ where $\frac{\pi}{2}<\text{A}<\pi$ and $\frac{3\pi}{2}<\text{B}<2\pi$ find$\tan\text{(A-B)}$.

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

Evaluate $\lim _{x \rightarrow 2}\left(\frac{x^2-4}{\sqrt{x+2}-\sqrt{3 x-2}}\right)$

Find $(x+1)^6+(x-1)^6$. Hence or otherwise evaluate $(\sqrt{2}+1)^6+(\sqrt{2}-1)^6$

Find the derivative of function $\frac{a x+b}{c x+d} ($it is to be understood that $a , b , c , d , p , q , r$ and $s$ are fixed non$-$zero constants and $m$ and $n$ are integers$).$

Find the sum of the first n terms of the series: $3 + 7 + 13 + 21 + 31 + ……….$