AP EAMCET · Maths · Continuity and Differentiability
If \(f(x)=|x|+|\sin x|\) for \(x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), then its left hand derivative at \(x=0\) is
- A 0
- B -1
- C -2
- D -3
Answer & Solution
Correct Answer
(C) -2
Step-by-step Solution
Detailed explanation
\begin{aligned} & f(x)=|x|+|\sin x| \\ & \text { LHD }=\lim _{h \rightarrow 0} \frac{f(0-h)-f(0)}{0-h} \\ & =\lim _{h \rightarrow 0} \frac{|0-h|+|\sin (0-h)|-(0+0)}{0-h} \\ & =\lim _{h \rightarrow 0} \frac{h+\sin h}{-h}=-\lim _{h \rightarrow 0}\left(1+\frac{\sin h}{h}\right) \\…
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
- \(\int \cos ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x=f(x)+C \Rightarrow f^{\prime}(a)=\)AP EAMCET 2022 Easy
- If \(f(x)=\left\{\begin{array}{ll}3 a x-2 b, & x\gt1 \\ a x+b+1, & x \lt 1\end{array}\right.\) and \(\lim _{x \rightarrow 1} f(x)\) exists, then the relation between \(a\) and \(b\) isAP EAMCET 2024 Easy
- If a function \(f(x)\) defined on \([a, b]\) is discontinuous at \(x=\alpha \in(a, b)\), thenAP EAMCET 2023 Easy
- If \(\alpha\) is a non-real root of \(x^6=1\), then \(\frac{\alpha^5+\alpha^3+\alpha+1}{\alpha^2+1}\) is equal toAP EAMCET 2005 Medium
- If the points having the position vectors \(-\hat{i}+4 \hat{j}-4 \hat{k}\), \(3 \hat{i}+2 \hat{j}-5 \hat{k},-3 \hat{i}+8 \hat{j}-5 \hat{k}\) and \(-3 \hat{i}+2 \hat{j}+\lambda \hat{k}\) are coplanar, then \(\lambda=\)AP EAMCET 2024 Easy
- A plane meets the \(X, Y, Z\)-axes in \(A, B, C\) respectively. If the centroid of the \(\triangle A B C\) is \((2,-3,5)\), then the perpendicular distance from origin to the given plane isAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- If \(\frac{\tan (\alpha+\beta-\gamma)}{\tan (\alpha-\beta+\gamma)}=\frac{\tan \gamma}{\tan \beta}\) and \(\beta \neq \gamma\), then the value of \(\sin 2 \alpha+\sin 2 \beta+\sin 2 \gamma\) isAP EAMCET 2017 Easy
- The following graph is obtained for a first order reaction (A \(\rightarrow\) P). The activation energy ( \(\mathrm{E}_{\mathrm{a}}\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) and heat of reaction ( \(|\Delta \mathrm{H}|\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) for this reaction are respectively
\(\left(\mathrm{x}=\right.\) reaction coordinate \(; \mathrm{y}=\mathrm{E}\) in \(\left.\mathrm{kJ} \mathrm{mol}^{-1}\right)\)
AP EAMCET 2025 Medium - Let \(\mathrm{A}\) and \(\mathrm{B}\) be two independent events of a random experiment. If the probability that both A and B occur is \(\frac{1}{6}\) and the probability that neither of them occur is \(\frac{1}{3}\), then the probability of occurrence of \(\mathrm{A}\) isAP EAMCET 2023 Hard
- Two concentric coils each of radius equal to are placed at right angles to each other. If and are the currents flowing through the coils, respectively, the magnetic induction at the center of the coils will beAP EAMCET 2021 Medium
- In a binomial distribution, if \(\mathrm{n}=4\) and \(\mathrm{P}(\mathrm{X}=0)=\frac{16}{81}\), then \(\mathrm{P}(\mathrm{X}=4)=\)AP EAMCET 2025 Medium
- \(\int_0^1 \frac{8 \log (1+x)}{1+x^2} d x=\)AP EAMCET 2020 Medium