COMEDK · Maths · 25. Continuity and Differentiability
If \(f(x)=\left\{\begin{array}{cc}{[x]+[-x],} & x \neq 2 \\ K, & x=2\end{array}\right.\), then \(f(x)\) is continuous at \(x=2\), provided \(K\) is equal to
- A 2
- B \(1 \quad\)
- C \(-1 \quad\)
- D 0
Answer & Solution
Correct Answer
(C) \(-1 \quad\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{cc}{[x]+[-x],} & x \neq 2 \\ K, & x=2\end{array}\right.\) Since, \(f(x)\) is continuous at \(x=2\) \(\therefore \lim _{x \rightarrow 2^{-}} f(x)=\lim _{x \rightarrow 2^{+}} f(x)=f(2)\) Now,…
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
- For an examination a candidate has to select 7 questions from three different groups \(\mathrm{A}, \mathrm{B}\) and C. The three groups contain 4, 5 and 6 questions respectively. In how many different ways can a candidate make his selection if he has to select atleast 2 questions from each group?COMEDK 2024 Medium
- Chords of the circle \(x^{2}+y^{2}=r^{2}\) touch the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\). The locus of the mid-points of the chords isCOMEDK 2017 Hard
- How many natural numbers are there between 100 and 1000 such that at least one of their digits is 6 ?COMEDK 2025 Medium
- There are 10 points in a plane out of which 4 points are collinear. How many straight lines can be drawn by joining any two of them?COMEDK 2023 Medium
- If \(f(x) = \begin{cases} \dfrac{\sqrt{1+x} - \sqrt{1-x}}{\sin x}, & x \neq 0 \\ k, & x = 0 \end{cases}\) is continuous at \(x = 0\), then \(k =\)COMEDK 2026 Medium
- If \(x=\frac{1-t}{1+t}, y=\frac{2 t}{1+t}\), then \(\frac{d^{2} y}{d x^{2}}=\)COMEDK 2012 Easy
More PYQs from COMEDK
- The atomic number of the element with highest ionisation energy among the following isCOMEDK 2012 Medium
- In the given circuit, if the barrier potential across the diode is 0.5 V , the current in the circuit is:
COMEDK 2025 Medium - A gaseous mixture consists of \(16 \mathrm{~g}\) of helium and \(16 \mathrm{~g}\) of oxygen. The ratio \(C_{p} / C_{V}\) of the mixture isCOMEDK 2020 Easy
- A solid cylinder of mass \(2 \mathrm{~kg}\) and radius \(0.2 \mathrm{~m}\) is rotating about its own axis without friction with angular velocity \(5 \mathrm{~rad} \mathrm{s}^{-1}\). A particle of mass \(1 \mathrm{~kg}\) moving with a velocity of \(5 \mathrm{~ms}^{-1}\) strikes the cylinder and sticks to it as shown in figure.
The angular velocity of the system after the particle sticks to it will beCOMEDK 2024 Medium - Presence of halogen in organic compounds can be detected usingCOMEDK 2020 Easy
- The length of the latus rectum of a conic \(49 y^2-16 x^2=784\) isCOMEDK 2025 Easy