If f(x) = frac{x}{1+|x|},for x in mathbb{R},t | vedclass

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

Question

(B) Given $f(x) = \frac{x}{1+|x|}$.To find $f^{\prime}(0)$,we use the definition of the derivative:$f^{\prime}(0) = \lim_{h 	o 0} \frac{f(0+h) - f(0)

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given $f(x) = \frac{x}{1+|x|}$.To find $f^{\prime}(0)$,we use the definition of the derivative:$f^{\prime}(0) = \lim_{h 	o 0} \frac{f(0+h) - f(0)}{h}$.Since $f(0) = \frac{0}{1+|0|} = 0$,we have:$f^{\prime}(0) = \lim_{h 	o 0} \frac{\frac{h}{1+|h|} - 0}{h} = \lim_{h 	o 0} \frac{1}{1+|h|}$.Now,we evaluate the left-hand and right-hand limits:Left-hand limit $(h 	o 0^-)$: $\lim_{h 	o 0^-} \frac{1}{1-h} = 1$.Right-hand limit $(h 	o 0^+)$: $\lim_{h 	o 0^+} \frac{1}{1+h} = 1$.Since both limits are equal,$f^{\prime}(0) = 1$.

If $f(x) = \frac{x}{1+|x|}$,for $x \in \mathbb{R}$,then $f^{\prime}(0)$ is equal to :

Similar Questions

If $y = x + \frac{1}{x}$,then which among the following holds?

If the function $g(x)$ is defined by $g(x) = \frac{x^{200}}{200} + \frac{x^{199}}{199} + \frac{x^{198}}{198} + \dots + \frac{x^2}{2} + x + 5$,then find $g'(0)$.

Find the derivative: $\frac{d}{dx} \left[ \log \left( x + \frac{1}{x} \right) \right] = $

Which one of the following is false?

If $\frac{d}{d x}\left[(x+1)\left(x^2+1\right)\left(x^4+1\right)\left(x^8+1\right)\right] = \left(15 x^p-16 x^q+1\right)(x-1)^{-2}$, then $(p, q)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module