lim _{x rightarrow pi / 2}(sec x-tan x) is eq | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) $\lim _{x ightarrow \frac{\pi}{2}}(\sec x-	an x)$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \left(\frac{1-\sin x}{\cos x}ight)$ (wh

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(D) $\lim _{x ightarrow \frac{\pi}{2}}(\sec x-	an x)$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \left(\frac{1-\sin x}{\cos x}ight)$ (which is of the $\frac{0}{0}$ form)Applying $L$'$H$ôpital's rule by differentiating the numerator and denominator with respect to $x$:$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \frac{\frac{d}{dx}(1-\sin x)}{\frac{d}{dx}(\cos x)}$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \frac{-\cos x}{-\sin x}$$\Rightarrow \lim _{x}$ ${ightarrow \frac{\pi}{2}} \cot x$Substituting $x = \frac{\pi}{2}$:$\Rightarrow \cot \frac{\pi}{2} = 0$

$\lim _{x \rightarrow \pi / 2}(\sec x-\tan x)$ is equal to

Similar Questions

If $\lim _{t}$ ${\rightarrow 0}\left(\int_0^1(3 x+5)^t d x\right)^{\frac{1}{t}}=\frac{\alpha}{5 e}\left(\frac{8}{5}\right)^{\frac{2}{3}}$,then $\alpha$ is equal to . . . . . .

$\mathop {\lim }\limits_{x \to \pi /4} \frac{{\sqrt 2 \cos x - 1}}{{\cot x - 1}} = $

$\lim _{x \rightarrow 3^{-}} \frac{x^3-3 x^2-4 x+12}{2 x^3-7 x^2+2 x+3} = $

The value of $\mathop {\lim }\limits_{x \to a} \frac{{\log (x - a)}}{{\log ({e^x} - {e^a})}}$ is

If $f(x) = 3x^{10} - 7x^8 + 5x^6 - 21x^3 + 3x^2 - 7$,then $\lim_{\alpha \rightarrow 0} \frac{f(1-\alpha) - f(1)}{\alpha^3 + 3\alpha} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module