mathop {lim }limits_{x to 0} frac{{sin (pi {{ | vedclass

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

Question

(B) આપણે લક્ષ $L = \mathop {\lim }\limits_{x 	o 0} \frac{{\sin (\pi {{\cos }^2}x)}}{{{x^2}}}$ ની કિંમત શોધવાની છે.$\cos^2 x = 1 - \sin^2 x$ હોવાથી,આપ

Vedclass · Accepted Answer

$\pi $

Vedclass · Answer

(B) આપણે લક્ષ $L = \mathop {\lim }\limits_{x 	o 0} \frac{{\sin (\pi {{\cos }^2}x)}}{{{x^2}}}$ ની કિંમત શોધવાની છે.$\cos^2 x = 1 - \sin^2 x$ હોવાથી,આપણે પદને આ રીતે લખી શકીએ:$L = \mathop {\lim }\limits_{x 	o 0} \frac{{\sin (\pi (1 - \sin^2 x))}}{{{x^2}}}$$L = \mathop {\lim }\limits_{x 	o 0} \frac{{\sin (\pi - \pi \sin^2 x)}}{{{x^2}}}$નિત્યસમ $\sin(\pi - 	heta) = \sin 	heta$ નો ઉપયોગ કરતા:$L = \mathop {\lim }\limits_{x 	o 0} \frac{{\sin (\pi \sin^2 x)}}{{{x^2}}}$અંશ અને છેદને $\pi \sin^2 x$ વડે ગુણતા અને ભાગતા:$L = \mathop {\lim }\limits_{x 	o 0} \left( \frac{{\sin (\pi \sin^2 x)}}{{\pi \sin^2 x}} ight) 	imes \frac{{\pi \sin^2 x}}{{{x^2}}}$જેમ $x 	o 0$,તેમ $\pi \sin^2 x 	o 0$,તેથી $\frac{{\sin (\pi \sin^2 x)}}{{\pi \sin^2 x}} 	o 1$.વળી,$\mathop {\lim }\limits_{x 	o 0} \frac{{\sin^2 x}}{{{x^2}}} = 1$.તેથી,$L = 1 	imes \pi 	imes 1 = \pi $.

$\mathop {\lim }\limits_{x \to 0} \frac{{\sin (\pi {{\cos }^2}x)}}{{{x^2}}} = $

Similar Questions

$\mathop {\lim }\limits_{x \to 0} {(\cos ax)^{\csc^2 bx}}$ ની કિંમત શોધો.

$\lim _{x \rightarrow 0} \left( \frac{\sin (\pi \cos ^2 x)}{x^2} \right) = $

$\lim _{x \rightarrow 0} \frac{x^2(\tan 2 x-2 \tan x)^2}{(1-\cos 2 x)^4}=$

આપેલ લક્ષની કિંમત શોધો: $\mathop {\lim }\limits_{x \to \pi } \frac{\sin (\pi-x)}{\pi(\pi-x)}$

$\mathop {\lim }\limits_{a \to 0} \frac{{\sin a - \tan a}}{{{{\sin }^3}a}}$ ની કિંમત શું થશે?

Vedclass Test Series

Exam Paper Generator

Online Exam Module