Let f:R to R be such that f(1) = 3 and f'(1) | vedclass

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

Question

(C) Let $L = \lim_{x 	o 0} \left\{ \frac{f(1 + x)}{f(1)} ight\}^{\frac{1}{x}}$.Taking natural logarithm on both sides,$\ln L = \lim_{x 	o 0} \frac

Vedclass · Accepted Answer

$e^2$

Vedclass · Answer

(C) Let $L = \lim_{x 	o 0} \left\{ \frac{f(1 + x)}{f(1)} ight\}^{\frac{1}{x}}$.Taking natural logarithm on both sides,$\ln L = \lim_{x 	o 0} \frac{1}{x} \ln \left( \frac{f(1 + x)}{f(1)} ight)$.Using the definition of the derivative or $L$'Hopital's rule,$\ln L = \lim_{x 	o 0} \frac{\ln f(1 + x) - \ln f(1)}{x}$.Applying $L$'Hopital's rule,$\ln L = \lim_{x 	o 0} \frac{f'(1 + x)}{f(1 + x)} = \frac{f'(1)}{f(1)}$.Given $f(1) = 3$ and $f'(1) = 6$,we have $\ln L = \frac{6}{3} = 2$.Therefore,$L = e^2$.

Let $f:R \to R$ be such that $f(1) = 3$ and $f'(1) = 6$. Then $\lim_{x \to 0} \left\{ \frac{f(1 + x)}{f(1)} \right\}^{\frac{1}{x}}$ equals

Similar Questions

If $r = [2\phi + \cos^2(2\phi + \pi/4)]^{1/2}$,then what is the value of the derivative $dr/d\phi$ at $\phi = \pi/4$?

Let $f(x)$ be a differentiable function for all $x \in R$ and $f(x+y)=f(x)+f(y)-3xy$. If $\lim _{h \rightarrow 0} \frac{f(h)}{h}=7$, then $f^{\prime}(x)=$

If $y = \frac{\tan x + \cot x}{\tan x - \cot x}$,then $\frac{dy}{dx} = $

Find the derivative: $\frac{d}{dx}\{ \cos(\sin(x^2)) \}$

Find the derivative: $\frac{d}{dx} \cosh^{-1}(\sec x) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module