mathop {lim }limits_{x to 0} frac{{{e^{sin x} | vedclass

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

Question

(A) हम जानते हैं कि $\mathop {\lim }\limits_{u 	o 0} \frac{e^u - 1}{u} = 1$ और $\mathop {\lim }\limits_{x 	o 0} \frac{\sin x}{x} = 1$.$\mathop {\lim

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) हम जानते हैं कि $\mathop {\lim }\limits_{u 	o 0} \frac{e^u - 1}{u} = 1$ और $\mathop {\lim }\limits_{x 	o 0} \frac{\sin x}{x} = 1$.$\mathop {\lim }\limits_{x 	o 0} \frac{e^{\sin x} - 1}{x} = \mathop {\lim }\limits_{x 	o 0} \left( \frac{e^{\sin x} - 1}{\sin x} 	imes \frac{\sin x}{x} ight)$$= \left( \mathop {\lim }\limits_{\sin x 	o 0} \frac{e^{\sin x} - 1}{\sin x} ight) 	imes \left( \mathop {\lim }\limits_{x 	o 0} \frac{\sin x}{x} ight)$$= 1 	imes 1 = 1$.वैकल्पिक रूप से,$L$-Hospital नियम का उपयोग करते हुए:$\mathop {\lim }\limits_{x 	o 0} \frac{e^{\sin x} - 1}{x} = \mathop {\lim }\limits_{x 	o 0} \frac{\frac{d}{dx}(e^{\sin x} - 1)}{\frac{d}{dx}(x)}$$= \mathop {\lim }\limits_{x 	o 0} \frac{\cos x \cdot e^{\sin x}}{1} = \cos(0) \cdot e^{\sin(0)} = 1 \cdot e^0 = 1$.

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\sin x}} - 1}}{x} = $

Similar Questions

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - {e^{ - x}}}}{{\sin x}}$ का मान है

$\mathop {\lim }\limits_{x \to 0} \,\frac{{{e^x} - x - 1}}{{{x^2}}}$ का मान है

$\lim _{x \rightarrow 2}(x-1)^{\frac{1}{3x-6}} = $

$\mathop {\lim }\limits_{x \to 0} \frac{{{e^{\tan x}} - {e^x}}}{{\tan x - x}} = $

$\lim _{x \rightarrow 0} \frac{1}{x^3} \int_0^x \frac{t \ln (1+t)}{t^4+4} dt$ का मान ज्ञात कीजिए।

Vedclass Test Series

Exam Paper Generator

Online Exam Module