_ x /2 [ x x - ( 2 ) x ] = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to \pi /2} \left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\sec x} \right] = $

A
$1$
✓
$-1$
C
$0$
D
None of these

✓

Answer

Correct option: B.

$-1$

b
(b) $\mathop {\lim }\limits_{x \to \pi /2} \,\left[ {x\tan x - \left( {\frac{\pi }{2}} \right)\,\sec x} \right]$

$ = \mathop {\lim }\limits_{x \to \pi /2} \,\,\frac{{2x\,\,\sin x - \pi }}{{2\,\cos x}}$, $\left[ {{\rm{form}} \,\, \frac{0}{0}} \right]$

$ = \mathop {\lim }\limits_{x \to \pi /2} \,\,\frac{{[2\,\sin x + 2x\cos x]}}{{ - 2\,\sin x}} = - 1$, (By $L -$ 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 "M.C.Q (1 Marks)" from STD 11 - 12. limits→STD 11 - 12. limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The acute angle between the lines $y = 3$ and $y = \sqrt 3 x + 9$ is .....$^o$

Let $a, b$ and $c$ be in $G.P$ with common ratio $r,$ where $a \ne 0$ and $0\, < \,r\, \le \,\frac{1}{2}$. If $3a, 7b$ and $15c$ are the first three terms of an $A.P.,$ then the $4^{th}$ term of this $A.P$ is

If $x$ is real, then the value of ${x^2} - 6x + 13$ will not be less than

If a be $\text{A.M.}$ and $p, q$ be two $\text{G.M.'s}$ between two numbers, then $2A$ is equal to:

If $\text{z}=\Big(\frac{1+\text{i}}{1-\text{i}}\Big),$ then $z^4$ equals:

For all $n\in N, 5^{2n}− 1$ is divisible by:

If a circle passes through the points of intersection of the coordinate axis with the lines $\lambda x - y + 1 = 0$ and $x - 2y + 3 = 0$, then the value of $\lambda $ is

$\lim_\limits{\text{x} \rightarrow \text{a}}\frac{\text{x}-\text{a}}{|\text{x}-\text{a}|}=$

If $sin\, \theta = sin\, \alpha$ then $sin\, \frac{\theta }{3}$ =

The number of terms with integral coefficients in the expansion of $\Big(17^{\frac{1}{3}}+35^{\frac{1}{2}}\text{x}\Big)^{600}$ is: