limlimits_{x rightarrow 2} frac{3^{x}+3^{3-x} | vedclass

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

Question

(B) माना $L = \lim _{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$.$t = 3^{x/2}$ प्रतिस्थापित करने पर,जब $x \rightarrow 2$,तब $t \righ

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(B) माना $L = \lim _{x ightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$.$t = 3^{x/2}$ प्रतिस्थापित करने पर,जब $x ightarrow 2$,तब $t ightarrow 3^{2/2} = 3$.अतः $3^x = t^2$ और $3^{3-x} = \frac{27}{t^2}$.साथ ही $3^{-x/2} = \frac{1}{t}$ और $3^{1-x} = \frac{3}{t^2}$.व्यंजक इस प्रकार होगा:$L = \lim _{t ightarrow 3} \frac{t^2 + \frac{27}{t^2} - 12}{\frac{1}{t} - \frac{3}{t^2}} = \lim _{t ightarrow 3} \frac{\frac{t^4 - 12t^2 + 27}{t^2}}{\frac{t - 3}{t^2}} = \lim _{t ightarrow 3} \frac{t^4 - 12t^2 + 27}{t - 3}$.अंश का गुणनखंड करने पर: $t^4 - 12t^2 + 27 = (t^2 - 9)(t^2 - 3) = (t - 3)(t + 3)(t^2 - 3)$.$L = \lim _{t ightarrow 3} \frac{(t - 3)(t + 3)(t^2 - 3)}{t - 3} = \lim _{t ightarrow 3} (t + 3)(t^2 - 3)$.$t = 3$ रखने पर: $L = (3 + 3)(3^2 - 3) = 6 	imes (9 - 3) = 6 	imes 6 = 36$.

$\lim\limits_{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$ का मान ज्ञात कीजिए।

Similar Questions

$\lim _{x \rightarrow 0} \frac{\sqrt{2}-\sqrt{1+\cos x}}{\sqrt{15+\cos 2x}-4} = $

$\mathop {\lim }\limits_{x \to \infty } (\sqrt {{a^2}{x^2} + ax + 1} - \sqrt {{a^2}{x^2} + 1})$ का मान क्या है?

$\lim _{x \rightarrow 0} \frac{\cos 4 x-4 \cos 2 x+3}{x^4} = $

यदि $f(x) = \frac{5x \operatorname{cosec}(\sqrt{x}) - 1}{(x - 2) \operatorname{cosec}(\sqrt{x})}$ है,तो $\lim_{x \rightarrow \infty} f(x^2) = $

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module