AP EAMCET · Maths · Differentiation
If \(f(x)=\frac{x}{1+|x|}\), for \(x \in R\), then \(f^{\prime}(0)\) is equal to :
- A 0
- B 1
- C 2
- D 3
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
We have, \(f(x)=\frac{x}{1+|x|}\) \(f^{\prime}(0)=\lim _{h \rightarrow 0} \frac{f(0+h)-f(0)}{h}\) \(=\lim _{h \rightarrow 0} \frac{\frac{h}{1+|h|}-0}{h}\) \(=\lim _{h \rightarrow 0} \frac{1}{1+|h|}=1\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(f: R \rightarrow R\) is defined by
\(f(x)=\left\{\begin{array}{cc}
\frac{2 \sin x-\sin 2 x}{2 x \cos x}, & \text { if } x \neq 0 \\
a, & \text { if } x=0
\end{array}\right. \text {, }\)
then the value of \(a\) so that \(f\) is continuous at 0 isAP EAMCET 2009 Medium - Let \(f: \mathrm{A} \rightarrow \mathrm{B}\) and \(g: \mathrm{B} \rightarrow \mathrm{C}\) be any two functions and \(g \circ f: \mathrm{A} \rightarrow \mathrm{C}\) is one-one, thenAP EAMCET 2017 Medium
- If \(c \in R\) be such that the line \(4 x-y+c=0\) touches the ellipse \(x^2+4 y^2=4\), then an equation having all such values of \(c\) among its roots isAP EAMCET 2019 Easy
- If \(y=\log _2\left(\log _2 x\right)\), then \(\frac{d y}{d x}\) is equal toAP EAMCET 2016 Medium
- If the point p represents the comple \(x\) number \(z=x+i y\) in the argand plane and if \(\frac{z+i}{z-1}\) is a purely imaginary number then the locus of \(p\) isAP EAMCET 2024 Hard
- Among the 4 digit numbers formed using the digits \(0,1,2,3,4\) when repetition of digits allowed, the number of numbers which are divisible by 4 isAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- The solution of \(\left(1+x^2\right) \frac{d y}{d x}+2 x y-4 x^2=0\) is :AP EAMCET 2006 Medium
- A galvanometer of resistance \(10 \Omega\) changes its range from \(1 \mathrm{~mA}\) to \(101 \mathrm{~mA}\) when a resistive wire is connected in parallel. If the resistivity of the material of the wire and its area of cross-section are \(1 \times 10^{-6} \Omega \mathrm{m}\) and \(1 \mathrm{~mm}^2\) respectively, then the length of the wire isAP EAMCET 2017 Easy
- Which of the following reactions is an example of roasting ?AP EAMCET 2025 Easy
- Butanone reacts with methyl magnesium bromide to form an addition product \((Z)\). On hydrolysis \(Z\) givesAP EAMCET 2018 Easy
- The solution set of \((5+4 \cos \theta)(2 \cos \theta+1)=0\) in the interval \([0,2 \pi]\), is :AP EAMCET 2003 Medium
- Two statements are given below.
Statement I: \(\mathrm{SnF}_4, \mathrm{PbF}_4\) are ionic in nature
Statement II: \(\mathrm{GeCl}_2\) is more stable than \(\mathrm{GeCl}_4\)
The correct answer isAP EAMCET 2024 Medium