WBJEE · Maths · Continuity and Differentiability
If \(f(x)=\left\{\begin{array}{ll}x^{3}-3 x+2, & x < 2 \\ x^{3}-6 x^{2}+9 x+2, & x \geq 2\end{array}\right.\) then
- A \(\lim _{x \rightarrow 2} f(x)\) does not exist
- B \(f\) is not continuous at \(x=2\)
- C \(f\) is continuous but not differentiable at \(x=2\)
- D \(t\) is continuous and differentiable at \(x=2\)
Answer & Solution
Correct Answer
(C) \(f\) is continuous but not differentiable at \(x=2\)
Step-by-step Solution
Detailed explanation
Given. \(f(x)=\left\{\begin{aligned} x^{3}-3 x+2, & x < 2 \\ x^{3}-6 x^{2}+9 x+2, & x \geq 2 \end{aligned}\right.\) LHL…
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
- An objective type test paper has 5 questions. Out of these 5 questions, 3 questions have four options each \((a, b, c, d)\) with one option being the correct answer. The other 2 questions have two options each, namely true and false. A candidate randomly ticks the options. Then, the probability that he/she will tick the correct option in atleast four questions, isWBJEE 2013 Easy
- Let \(f(x)=\left[x^2\right] \sin \pi x, x > 0\). ThenWBJEE 2023 Easy
- The integrating factor of the differential equation \(3 x \log _{e} x \frac{d y}{d x}+y=2 \log _{e} x\) is given byWBJEE 2012 Hard
- In a triangle \(\mathrm{PQR}, \angle \mathrm{R}=\pi / 2\). If \(\tan \left(\frac{\mathrm{p}}{2}\right)\) and \(\tan \left(\frac{\mathrm{Q}}{2}\right)\) are roots of \(\mathrm{ax}^2+\mathrm{bx}+\mathrm{c}=0\), where \(\mathrm{a} \neq 0\), then which one is true ?WBJEE 2010 Medium
- The slope at any point of a curve \(y=f(x)\) is given by \(\frac{d y}{d x}=3 x^2\) and it passes through \((-1,1)\). The equation of the curve isWBJEE 2009 Easy
- Let \(\mathrm{A}=\left(\begin{array}{ccc}12 & 24 & 5 \\ \mathrm{x} & 6 & 2 \\ -1 & -2 & 3\end{array}\right) .\) The value of \(\mathrm{x}\) for which the matrix \(\mathrm{A}\) is not invertible isWBJEE 2020 Easy
More PYQs from WBJEE
- If the \(n\) terms \(a_1, a_2, \ldots \ldots \ldots . ., a_n\) are in A.P. with increment \(r\), then the difference between the mean of their squares & the square of their mean isWBJEE 2023 Medium
- \(\mathrm{BrF}_3\) self ionises as followingWBJEE 2023 Easy
- Let \(y\) be the solution of the differential equation
\(x \frac{d y}{d x}=\frac{y^{2}}{1-y \log x}\) satisfying \(y(1)=1 .\) Then, \(y\)
satisfiesWBJEE 2012 Medium - A light charged particle is revolving in a circle of radius \(r\) in electrostatic attraction of a static heavy particle with opposite charge How does the magnetic field vary at the centre of the circle due to the moving charge depend on \(r ?\)WBJEE 2018 Medium
- The least value of \(2 x^{2}+y^{2}+2 x y+2 x-3 y+8\) for real
numbers \(x\) and \(y,\) isWBJEE 2015 Easy - A point moves, so that the sum of squares of its distance from the points (1,2) and (-2,1) is always \(6 .\) Then, its locus isWBJEE 2013 Medium