Evaluate the following limit: _ x 2 2x - Vidyadip

Question

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\sin2\text{x}}{\cos\text{x}}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow{\frac{\pi}{2}}}\frac{\sin2\text{x}}{\cos\text{x}}$ $=\lim\limits_{\text{x}\rightarrow\frac{\pi}{2}}\frac{2\sin\text{x}\cos\text{x}}{\cos\text{x}}$ $=2\lim\limits_{\text{x}\rightarrow\frac{\pi}{2}}\sin\text{x}$ $=2\times\sin\frac{\pi}{2}$ $=2\times1$ $=2$

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 "2 Marks Questions" from Limits→Limits — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

For each of the following compound statements first identify the connecting words and then break it into component statements.
$x = 2$ and $x = 3$ are the roots of the equation $3x^2 – x – 10 = 0.$

Find the derivative of the function $\frac{x^{2} \cos \left(\frac{\pi}{4}\right)}{\sin x}$ (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers)

Solve the following linear inequations in R:
$3\text{x}+9\geq-\text{x}+19$

Show thet the followiong sequences is an A.P. Also, find the common difference and write 3 more terms in each case.
$-1,\frac{1}{4},\frac{3}{2},\frac{11}{4},...$

An integer is chosen at random from the numbers ranging from $1$ to $50$. What is the probability that the integer chosen is a multiple of $2$ or $3$ or $10$ ?

A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.

Solve: $\tan 2 x=-\cot \left(x+\frac{\pi}{3}\right)$

What can be said regarding a line if its slope is:

Zero.
Positive.
Negative?

Find the centre and radius of the circle. $x ^2 + y ^2 - 8x - 10y - 12 = 0$

Find: $n^{th}$ term of the A.P. $13, 8, 3, -2, ...$