Evaluate: _ x 0 1- 2 x x^2 . - Vidyadip

Question

Evaluate: $\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{x^2}$.

✓

Answer

We have to find the value of
$\begin{array}{l}\lim _{x \rightarrow 0} \frac{1-\cos 2 x}{x^2}=\lim _{x \rightarrow 0} \frac{2 \sin ^2 x}{x^2} \\ =2 \lim _{x \rightarrow 0}\left(\frac{\sin x}{x} \times \frac{\sin x}{x}\right)=2 \lim _{x \rightarrow 0} \frac{\sin x}{x} \times \lim _{x \rightarrow 0} \frac{\sin x}{x}=2(1)(1)=2\end{array}$

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 Model Paper 5→Model Paper 5 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evaluate $\lim _{x \rightarrow \pi} \frac{\sin ^2 2 x}{\cos ^2 \frac{1}{2} x}.$

Find the sum of the following series to infinity:

$\frac{2}{5}+\frac{3}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+\ ... \infty$

If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?
[Hint: In each case number of words beginning with A, C, H, I is 5!]

How many three-digit numbers are there?

Solve the following system of equations in R.
x - 2 > 0, 3x < 18

If a is the G.M. of 2 and $\frac14,$ find a.

For some constants a and b, find the derivative of (x - a)(x - b)

Find $\lim\limits_{\text{x}\rightarrow1}\text{f(x)}$ if $\text{f(x)}=\begin{cases}\text{x}^2-1, & \text{x} \le1\\-\text{x}^2-1, &\text{x} > 1\end{cases}.$

For all sets A and B, $(\text{A} - \text{B}) \cup (\text{A} \cap \text{B}) = \text{A}$

Find the general solutions of the following equations:
$\sqrt{3}\sec\text{x}=2$