_ x /2 1 + 2x ( - 2x) ^2 = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to \pi /2} \frac{{1 + \cos 2x}}{{{{(\pi - 2x)}^2}}} = $

A
$1$
B
$2$
C
$3$
✓
$\frac{1}{2}$

✓

Answer

Correct option: D.

$\frac{1}{2}$

d
(d) $\pi - 2x = \theta \,\, \Rightarrow \,\,x = \frac{\pi }{2} - \frac{\theta }{2}$

and as $x \to \,(\pi /2),\,\,\theta \to 0$

Now solve yourself.

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 12. limits→12. limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The difference between the lengths of the major axis and the latus-rectum of an ellipse is

For a frequency distribution standard deviation is computed by applying the formula:

A bag contains 3 black, 4 white and 2 red balls, all the ballsbeing different.Number of selections of atmost 6 balls containing balls of all the colours is:

The real roots of the equation $cos^7x\, +\, sin^4x\, =\, 1$ in the interval $(-\pi, \pi)$ are

The fractional value of 2.357 is:

India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point $0, 1$ and $2$ are $0.45, 0.05$ and $0.50$ respectively. Assuming that the outcomes are independents, the probability of India getting at least $7$ points is

If the coefficients of $x^4, x^5$ and $x^6$ in the expansion of $(1+x)^n$ are in the arithmetic progression, then the maximum value of $n$ is :

The probability of happening an event $A$ in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is

$\sin (\pi + \theta )\sin (\pi - \theta )\,{\rm{ cose}}{{\rm{c}}^2}\theta = $

Circumcenter of the triangle formed by the line $y = x,\;\;y = 2x$ and $y = 3x + 4$ is