If f(x)=x/(1+|x|) , for x ∈ R , then f^′(0) is equal to :

Correct answer: (B) 1. We have, f(x)=x/(1+|x|) f^′(0)=lim _h arrow 0 (f(0+h)-f(0))/h =lim _h arrow 0 (h/(1+|h|)-0)/h =lim _h arrow 0 1/(1+|h|)=1

Q76 / 160 · TS EAMCET 2003 · Mathematics

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

A
0
Correct answer
B
1
C
2
D
3

Solution

We have, $f(x)=\frac{x}{1+|x|}$ $f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}$ $=\lim _{h \rightarrow 0} \frac{\frac{h}{1+|h|}-0}{h}$ $=\lim _{h \rightarrow 0} \frac{1}{1+|h|}=1$

Hence, the correct answer is option: 'B'.

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

Solution

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