(B) For $f(x)$ to be continuous at $x = 0$,we must have $f(0) = \lim_{x \to 0} f(x)$.$f(0) = \lim_{x \to 0} \frac{2^{x}-1}{1-3^{x}}$$f(0) = \lim_{x \t

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(B) For $f(x)$ to be continuous at $x = 0$,we must have $f(0) = \lim_{x \to 0} f(x)$.$f(0) = \lim_{x \to 0} \frac{2^{x}-1}{1-3^{x}}$$f(0) = \lim_{x \to 0} \frac{2^{x}-1}{-(3^{x}-1)}$$f(0) = -\frac{\lim_{x \to 0} \frac{2^{x}-1}{x}}{\lim_{x \to 0} \frac{3^{x}-1}{x}}$Using the standard limit $\lim_{x \to 0} \frac{a^{x}-1}{x} = \log a$,we get:$f(0) = -\frac{\log 2}{\log 3}$

Class 12 Mathematics Continuity and Differentiation Continuity

Easy

If $f(x) = \left(\frac{2^{x}-1}{1-3^{x}}\right)$ for $x \neq 0$ is continuous at $x = 0$,then $f(0) = $

MHT CET 2020 All MHT CET

A
$-\log_{3} 2$
B
$-\frac{\log 2}{\log 3}$
C
$\frac{\log 2}{\log 3}$
D
$-\log 2$

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Continuity and Differentiation

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