KCET · Maths · Definite Integration
\( f(x)=\left\{\begin{array}{cl}3 x-8 & \text { if } x \leq 5 \\ 2 k & \text { if } x>5\end{array}\right. \) is continuous, find \( k . \)
- A \( \frac{2}{7} \)
- B \( \frac{3}{7} \)
- C \( \frac{4}{7} \)
- D \( \frac{7}{2} \)
Answer & Solution
Correct Answer
(D) \( \frac{7}{2} \)
Step-by-step Solution
Detailed explanation
Given that, \(f(x)=\left\{\begin{array}{cc}3 x-8 & x \leq 5 \\ 2 k & x>5\end{array}\right.\)
At \(x=5\), we have \(f(5)=3(5)-8=7\)
Taking R.H.L, we have
\(\lim _{x \rightarrow 5} 2 k=2 k\)
\(\mathrm{WE}\) know that for continuous L.H.L \(=\) R.H.L.
Therefore, \(7=2 k \Rightarrow k=\frac{7}{2}\)
At \(x=5\), we have \(f(5)=3(5)-8=7\)
Taking R.H.L, we have
\(\lim _{x \rightarrow 5} 2 k=2 k\)
\(\mathrm{WE}\) know that for continuous L.H.L \(=\) R.H.L.
Therefore, \(7=2 k \Rightarrow k=\frac{7}{2}\)
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 \(f(x)=\cos ^{-1}\left[\frac{1}{\sqrt{13}}(2 \cos x-3 \sin x)\right]\). Then, \(f^{\prime}(0.5)\) is equal toKCET 2013 Medium
- A flashlight has \( 10 \) batteries out of which \( 4 \) are dead. If \( 3 \) batteries are selected without
replacement andtested, then the probability that all \( 3 \) are dead isKCET 2018 Easy - Consider an infinite geometric series with first term ' \( a \) ' and common ratio ' \( r \) '. If the sum is \( 4 \) and
the second term is \( \frac{3}{4} \), thenKCET 2014 Hard - The number of ways in which \( 5 \) girls and \( 3 \) boys can be seated in a row so that no two boys
are togetherisKCET 2018 Easy - The value of the integral
\(\int_{0}^{\pi / 2}\left(\sin ^{100} x-\cos ^{100} x\right) d x\) isKCET 2007 Easy - \( \int \frac{1}{x^{2}\left(x^{4}+1\right)^{3 / 4}} \mathrm{dx} \) is equal toKCET 2015 Medium
More PYQs from KCET
- If \(y=(x-1)^{2}(x-2)^{3}(x-3)^{5}\), then \(\frac{d y}{d x}\) at \(x=4\) is equal toKCET 2021 Medium
- Which one of the following is correct for all elements from Sc to Cu?KCET 2021 Medium
- An engine moving towards a wall with a velocity \(50 \mathrm{~ms}^{-1}\) emits a note of \(1.2 \mathrm{kHz}\). Speed of sound in air is \(350 \mathrm{~ms}^{-1}\). The frequency of the note after reflection from the wall as heard by the driver of the engine isKCET 2007 Hard
- The waves used for line-of-sight (LOS) communication isKCET 2015 Hard
- The solution set of the inequation \( \frac{x^{2}+6 x-7}{|x+4|} < 0 \) isKCET 2015 Hard
- Mercury is a liquid metal becauseKCET 2008 Easy