Evaluate: _ x 0 ^ 2 2x ^ 2 4x - Vidyadip

Question

Evaluate:
$\lim\limits_{\text{x} \rightarrow 0}\frac{\sin^{2}2\text{x}}{\sin^{2}4\text{x}}$

✓

Answer

Given that $\lim\limits_{\text{x} \rightarrow 0}\frac{\sin^{2}2\text{x}}{\sin^{2}4\text{x}}$
$=\lim\limits_{\text{x} \rightarrow 0}\frac{\sin^{2}2\text{x}}{\sin^{2}2(2\text{x})}$
$=\lim\limits_{\text{x} \rightarrow 0}\frac{\sin^{2}2\text{x}}{4\sin^{2}2\text{x}.\cos^{2}2\text{x}}$
$=\frac{1}{4.\cos^{2}2\text{x}}$
Taking limits we have
$=\frac{1}{4.\cos^{2}0}=\frac{1}{4}$
Hence, the required is $\frac{1}{4.}$

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 "2 Marks Questions" from Limits and Derivatives→Limits and Derivatives — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

The centroid of a triangle ABC is at the point (1, 1, 1). If the coordinates of A and B are (3, –5, 7) and (–1, 7, – 6), respectively, find the coordinates of the point C.

Evaluate $\lim _{x \rightarrow \frac{\pi}{2}} \frac{1+\cos 2 x}{(\pi-2 x)^2}.$

The sum of three numbers which are consecutive terms of an A.P. is 21. If the second number is reduced by 1 and the third is increased by 1, we obtain three consecutive terms of a G.P. Find the numbers.

Prove that:
$\sec\Big(\frac{3\pi}{2}-\text{x}\Big)\sec\Big(\text{x}-\frac{5\pi}{2}\Big)+\tan\Big(\frac{5\pi}{2}+\text{x}\Big)\tan\Big(\text{x}-\frac{3\pi}{2}\Big)=-1$

Three coins are tossed together,find the probability of getting:

At least one head and one tail.

Write the complex number $\frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}$ in the form of $a+i b$.

In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics?

Find the slope of the line, which makes an angle of 30° with the positive direction of y-axis measured anticlockwise.

Find the equation to the straight line which cuts off equal positive intercepts on the axes and their product is 25.

Show the following quadratic equation by factorization method:
$\text{x}^2-(2\sqrt{3}+3\text{i}))\text{x}+6\sqrt{3}\text{ i}=0$