_ x 9 ( x^ 3 / 2 -27 x-9 )= - Vidyadip

MCQ

$\lim _{x \rightarrow 9}\left(\frac{x^{3 / 2}-27}{x-9}\right)=$

A
$\frac{3}{2}$
✓
$\frac{9}{2}$
C
$\frac{2}{3}$
D
$\frac{1}{3}$

✓

Answer

Correct option: B.

$\frac{9}{2}$

(B)
$\lim _{x \rightarrow 9}\left(\frac{x^{3 / 2}-27}{x-9}\right)$
$=\lim _{x \rightarrow 9}\left(\frac{(\sqrt{x})^3-3^3}{(\sqrt{x}+3)(\sqrt{x}-3)}\right)$
$=\lim _{x \rightarrow 9}\left(\frac{(\sqrt{x}-3)(x+3 \sqrt{x}+9)}{(\sqrt{x}+3)(\sqrt{x}-3)}\right)$
$=\frac{9+3 \sqrt{9}+9}{\sqrt{9}+3}$
$=\frac{27}{6}$
$=\frac{9}{2}$

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

Out of $30$ consecutive integers, $2$ are chosen at random. The probability that their sum is odd, is

For suitable matrices A, B, the false statement is ___________

If one root of the equation $x^2+ px + 12 = 0$, is $4,$ while the equation $x^2+ px + q = 0$ has equal roots, the value of $q$ is:

If $x=1+2 i$, the value of $x^3+2 x^2-3 x+5=$

The domain of the function $\text{f(x)}=\sqrt{2-2\text{x}-\text{x}^2}$ is :

The value of $(8)^{1 / 3}$ is

$\lim _{x \rightarrow 1} \frac{x^{100}-1}{x^{50}-1}=$

The probability that in a throw of two dice we get, an even sum or sum less than 5 is,

If $A, B, C$ are the angles of $\triangle A B C$, then $\cot A \cdot \cot B+$ $\cot B \cdot \cot C+\cot C \cdot \cot A=$

There are 6 positive and 8 negative numbers. From these four numbers are chosen at random and multiplied. Then the probability, that the product is negative number, is