Let f(x) be a differentiable function at x=a | vedclass

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

Question

(B) Given $f^{\prime}(a) = 2$ and $f(a) = 4$. We need to evaluate $L = \lim_{x \rightarrow a} \frac{x f(a) - a f(x)}{x - a}$. Since the limit is of th

Vedclass · Accepted Answer

$4 - 2a$

Vedclass · Answer

(B) Given $f^{\prime}(a) = 2$ and $f(a) = 4$. We need to evaluate $L = \lim_{x \rightarrow a} \frac{x f(a) - a f(x)}{x - a}$. Since the limit is of the form $\frac{0}{0}$,we apply $L$'$H$ôpital's rule by differentiating the numerator and denominator with respect to $x$: $L = \lim_{x \rightarrow a} \frac{\frac{d}{dx}(x f(a) - a f(x))}{\frac{d}{dx}(x - a)}$ $L = \lim_{x \rightarrow a} \frac{f(a) - a f^{\prime}(x)}{1}$ Substituting $x = a$: $L = f(a) - a f^{\prime}(a)$ $L = 4 - a(2) = 4 - 2a$.

$I$. $f'(x) = \frac{3}{4}x^{4/3} + 9$	$II$. $f(x) = \frac{9}{28}x^{7/3} - 2$
$III$. $f(x) = \frac{9}{28}x^{7/3} + 6$	$IV$. $f'(x) = \frac{3}{4}x^{4/3} - 4$

Let $f(x)$ be a differentiable function at $x=a$ with $f^{\prime}(a)=2$ and $f(a)=4$. Then $\lim _{x \rightarrow a} \frac{x f(a)-a f(x)}{x-a}$ equals ...... .

Similar Questions

Let $f$ and $g$ be differentiable functions on $R$ such that $f \circ g$ is the identity function. If for some $a, b \in R$,$g^{\prime}(a) = 5$ and $g(a) = b$,then $f^{\prime}(b)$ is equal to

If $f(t) = \frac{1 + \operatorname{cosec} t}{1 - \operatorname{cosec} t}$ for $0 < t < \frac{\pi}{2}$ and $f^{\prime}(t) = f(t) g(t)$,then $g(t) =$

Differentiate the following with respect to $x$: $e^{\sin ^{-1} x}$

Which of the following statements could be true if $f''(x) = x^{1/3}$?

$I$. $f'(x) = \frac{3}{4}x^{4/3} + 9$ $II$. $f(x) = \frac{9}{28}x^{7/3} - 2$

$III$. $f(x) = \frac{9}{28}x^{7/3} + 6$ $IV$. $f'(x) = \frac{3}{4}x^{4/3} - 4$

If $G(x) = -\sqrt{25-x^{2}}$,then $\lim _{x \rightarrow 1} \frac{G(x)-G(1)}{x-1}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module