Evaluate the following one sided limits: _ x - 2^+ - Vidyadip

Question

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow\frac{-\pi}{2^+}}\sec\text{x}$

✓

Answer

$\lim\limits_{\text{x}\rightarrow\frac{\pi^+}{2}}\sec\text{x}$
$=\lim\limits_{\text{h}\rightarrow0}\sec\big(-\frac{\pi}{2}+\text{h}\big)$
$=\sec\Big(-\frac{\pi}{2}+0\Big)$
$=\sec\Big(-\frac{\pi}{2}\Big)$
$=\frac{1}{\cos\Big(-\frac\pi2\Big)}$
$=\frac{-1}{\Big(\cos\frac{\pi}{2}\Big)}$
$\Rightarrow\frac{-1}{0}=-\infty$

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 "Solve the Following Question.(2 Marks)" from Limits→Limits — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the magnitude, in radians and degrees, of the interior angle of a regular.
heptagon.

A family has two children. Find the probability that both the children are girls, given that at least one of them is a girl.

Find the number of seating arrangements for 3 men and 3 women to sit around a table so that exactly two women are together.

Find the equation of tangent to the ellipse : $\frac{x^2}{8}+\frac{y^2}{6}=1$ at the point $(2, \sqrt{3})$.

Differentiate the following w.r.t. x :
$y=\log x-\operatorname{cosec} x+5^x-\frac{3}{x^{\frac{3}{2}}}$

Find the equation of the line: passing through the origin and parallel to AB, where A is (2,4) and B is (1,7).

$\sum_{r=1}^{\infty}\left(-\frac{1}{3}\right)^T$

Prove the following identities:
$\sec^4\text{x}− \sec^2\text{x}= \tan^4\text{x}+\tan^2\text{x}$

Find the centre and radius of each of the following circles:
$x^2+y^2-6 x-8 y-24=0$

Find the distance of the point (2, 3) from the line 2x - 3y + 9 = 0 measured along a line making an angle of 45° with the x-axis.