_ x 3 (x-3 x-2-4-x )= - Vidyadip

MCQ

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

✓
1
B
2
C
-1
D
-2

✓

Answer

Correct option: A.

1

(A)
$\lim _{x \rightarrow 3}\left(\frac{x-3}{\sqrt{x-2}-\sqrt{4-x}}\right)$
$=\lim _{x \rightarrow 3} \frac{(x-3)(\sqrt{x-2}+\sqrt{4-x})}{(\sqrt{x-2}-\sqrt{4-x})(\sqrt{x-2}+\sqrt{4-x})}$
$=\lim _{x \rightarrow 3} \frac{(x-3)(\sqrt{x-2}+\sqrt{4-x})}{2(x-3)}$
$=1$
Alternate method:
Apply L-Hospital's rule.

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 "MCQ" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $e$ and $e^{\prime}$ are eccentricities of two conics of same type and $e ^2+ e ^{\prime 2}=3$, then they must be

A straight line makes an intercept on the Y-axis twice as long as that on X-axis and is at a unit distance from the origin. Then the line is represented by the equations

If $z=-1-i$, then $\arg z$ is

If the function $f:[1, \infty) \rightarrow[1, \infty)$ is defined by $f(x)=2^{x(x-1)}$, then $f^{-1}(x)$ is

If A and B are two events such that $P(A \cup B)=P(A \cap B)$, then the true relation is

If $(1+\text{i})(1+2\text{i})(1+3\text{i})...(1+\text{ni})=\text{a}+\text{ib},$ then $2.5.10.17 ... (1+\text{n}^2)=$

The number of values of $x$ in $[0,\ 2\pi]$ that satisfy the equation $\sin^2\text{x}-\cos\text{x}=\frac{1}{4}$

The distance between the vertex and the focus of the parabola $x^2-2 x+3 y-2=0$ is

If three dice are throw simultaneously, then the probability of getting a score of $5$ is :

If$A+B=225^{\circ}$,then$\frac{cotA}{1+cotA}\cdot\frac{cotB}{1+cotB}=$