lim _{x rightarrow frac{pi}{2}} frac{(1-sin x | vedclass

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

Question

(C) ધારો કે $L = \lim _{x \rightarrow \frac{\pi}{2}} \frac{(1-\sin x)(8 x^3-\pi^3) \cos x}{(\pi-2 x)^4}$.આપણે પદાવલિને આ રીતે લખી શકીએ:$L = \lim _{x \

Vedclass · Accepted Answer

$\frac{-3 \pi^2}{16}$

Vedclass · Answer

(C) ધારો કે $L = \lim _{x \rightarrow \frac{\pi}{2}} \frac{(1-\sin x)(8 x^3-\pi^3) \cos x}{(\pi-2 x)^4}$.આપણે પદાવલિને આ રીતે લખી શકીએ:$L = \lim _{x \rightarrow \frac{\pi}{2}} \frac{(1-\sin x)(2x-\pi)(4x^2+\pi^2+2\pi x) \cos x}{16(\frac{\pi}{2}-x)^4}$.ધારો કે $x - \frac{\pi}{2} = h$,તેથી $x = \frac{\pi}{2} + h$. જેમ $x \rightarrow \frac{\pi}{2}$,તેમ $h \rightarrow 0$.ત્યારે $\cos x = \cos(\frac{\pi}{2} + h) = -\sin h$ અને $1 - \sin x = 1 - \sin(\frac{\pi}{2} + h) = 1 - \cos h$.વળી,$2x - \pi = 2(\frac{\pi}{2} + h) - \pi = 2h$.આ કિંમતો લક્ષમાં મૂકતા:$L = \lim _{h}$ ${\rightarrow 0} \frac{(1-\cos h)(2h)(4(\frac{\pi}{2}+h)^2 + \pi^2 + 2\pi(\frac{\pi}{2}+h))(-\sin h)}{16(-h)^4}$.$L = \lim _{h \rightarrow 0} \frac{-(1-\cos h)}{h^2} \cdot \frac{\sin h}{h} \cdot \frac{2h(3\pi^2 + 8\pi h + 4h^2)}{16h}$.$L = -(\frac{1}{2}) \cdot (1) \cdot \frac{2(3\pi^2)}{16} = -\frac{3\pi^2}{16}$.

$\lim _{x \rightarrow \frac{\pi}{2}} \frac{(1-\sin x)(8 x^3-\pi^3) \cos x}{(\pi-2 x)^4}$

Similar Questions

$\lim _{x \rightarrow 0} \frac{\tan 2x - 2\tan x}{(1 - \cos x)(2^x - 1)} = $

$\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{\sin ^4 x} = $

$\lim _{x \rightarrow a} \frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}$ ની કિંમત શોધો.

જો $L = \lim_{x^2 \to a} \frac{b - \cos(x^2 - a)}{(x^2 - a) \sin(c(x^2 - a))}$ એ શૂન્યતર શાંત કિંમત $(a > 0)$ હોય,તો:

$\mathop {{\rm{lim}}}\limits_{x \to 0} \frac{{\left( {1 - \cos 2x} \right)\left( {3 + \cos x} \right)}}{{x\tan 4x}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module