WBJEE · Maths · Continuity and Differentiability
\(\operatorname{Let} f(x)=\left\{\begin{array}{l}0, \text { if }-1 \leq x < 0 \\ 1, \text { if } x=0 \\ 2, \text { if } 0 < x \leq 1\end{array}\right.\) and let \(F(x)=\int_{-1}^{x} f(t) d t,-1 \leq x \leq 1\), then
- A \(\mathrm{F}\) is continuous function in \([-1,1]\)
- B \(F\) is discontinuous function in \([-1,1]\)
- C \(\mathrm{F}^{\prime}(\mathrm{x})\) exists at \(\mathrm{x}=0\)
- D \(\mathrm{F}^{\prime}(\mathrm{x})\) does not exists at \(\mathrm{x}=0\)
Answer & Solution
Correct Answer
(D) \(\mathrm{F}^{\prime}(\mathrm{x})\) does not exists at \(\mathrm{x}=0\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{ll}0 & -1 \leq x \(F(x)=\left\{\begin{array}{ll}0 & -1 \leq x \leq 0 \\ 2 x & 0 < x \leq 1\end{array}\right.\)
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
- A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a timet is given by \(s=t^{2}+a t-b+17,\) where \(a\) and \(b\) are real numbers. If the particle comes to rest after 5s at a distance of \(s=25\) units from the fixed point, then values of \(a\) and \(b\) are. respectivelyWBJEE 2015 Easy
- In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. In how many ways can they do so if the lift does not stop at the second floor?WBJEE 2020 Easy
- If the equation \(x^{2}-ca+d=0\) has roots equal to the fourth powers of the roots of \(x^{2}+a x+b=0,\) where \(a^{2}>4 b,\) then the roots of \(x^{2}-4 b x+2 b^{2}-c=0\) will beWBJEE 2018 Medium
- The area of the region \(\left\{(x, y): x^{2}+y^{2} \leq 1 \leq x+y\right\}\) isWBJEE 2020 Medium
- Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while \(\log \left(\frac{5 c}{2 a}\right), \log \left(\frac{7 b}{5 c}\right), \log \left(\frac{2 a}{7 b}\right)\) are in A.P. Then \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are the lengths of the sides ofWBJEE 2021 Medium
- Let \(\hat{\alpha}, \hat{\beta}, \hat{\gamma}\) be three unit vectors such that \(\hat{\alpha} \times (\hat{\beta} \times \hat{\gamma})=\frac{1}{2}(\hat{\beta}+\hat{\gamma})\) where \(\hat{\alpha} \times(\hat{\beta} \times \hat{\gamma})=(\hat{\alpha} \cdot \hat{\gamma}) \hat{\beta}-(\hat{\alpha} \cdot \hat{\beta}) \gamma \cdot\) If \(\hat{\beta}\) is not parallel to \(\hat{\gamma},\) then the angle between \(\hat{\alpha}\) and \(\hat{\beta}\) isWBJEE 2019 Medium
More PYQs from WBJEE
- If a person can throw a stone to maximum height of \(\mathrm{h}\) metre vertically, then the maximum distance through which it can be thrown horizontally by the same person isWBJEE 2011 Medium
- If \(\theta \in\left(\frac{\pi}{2}, \frac{3 \pi}{2}\right)\) then the value of \(\sqrt{4 \cos ^{4} \theta+\sin ^{2} 2 \theta}+4 \cot \theta \cos ^{2}\left(\frac{\pi}{4}-\frac{\theta}{2}\right)\) isWBJEE 2015 Hard
- Let \(f\) and \(g\) be differentiable on the interval \(I\) and let \(a, b \in I, a < b\). Then,WBJEE 2019 Medium
- Let \(f\) be a non-negative function defined on \(\left[0, \frac{\pi}{2}\right]\). If \(\int_0^x\left(f^{\prime}(t)-\sin 2 t\right) d t=\int_x^0 f(t) \tan t d t, f(0)=1\), then \(\int_0^{\frac{\pi}{2}} f(x) d x\) isWBJEE 2023 Hard
- Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the external pressure is \(\mathrm{P}\), then surface tension of the bubbles isWBJEE 2021 Medium
- An object placed at a distance of \(16 \mathrm{cm}\) from a \(\begin{array}{llll}\text { convex lens } & \text { produces } & \text { an image } & \text { of }\end{array}\) magnification \(m(m>1)\). If the object is moved towards the lens by \(8 \mathrm{cm}\), then again an image of magnification \(m\) is obtained. The numerical value of the focal length of the lens isWBJEE 2013 Hard