TS EAMCET · Maths · Continuity and Differentiability
Assertion (A) \(f(x)=|x-a|+|x-b|\), is continuous on \(\mathbf{R}\)Reason (R) \(\frac{|x-\alpha|}{x-\alpha}\) is continuous at \(x \in \mathbf{R}-\{\alpha\}\). The correct option among the following is
- A (A) is true, (R) is true and (R) is the correct explanation for \(\mathrm{A}\)
- B \((\mathrm{A})\) is true, \((\mathrm{R})\) is true but \((\mathrm{R})\) is not the correct explanation for \(A\)
- C \((A)\) is true but \((R)\) is false
- D (A) is false but \((R)\) is true
Answer & Solution
Correct Answer
(B) \((\mathrm{A})\) is true, \((\mathrm{R})\) is true but \((\mathrm{R})\) is not the correct explanation for \(A\)
Step-by-step Solution
Detailed explanation
The function \(f(x)=|x-a|+|x-b|\) is continuous on \(R\). The function \(\frac{|x-\alpha|}{x-\alpha}\) is continuous at \(x \in \mathbf{R}-\{\alpha\}\)
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
- The probability distribution of a random variable \(X\) is given below
The variance of \(X\) isTS EAMCET 2017 Medium - TS EAMCET 2019 Medium
- If the coefficient of in the expansion of is , thenTS EAMCET 2020 Medium
- Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined by \(f(x)=5^{-|x|}+\operatorname{sgn}\left(5^{-x}\right)\), where \(\operatorname{sgn} x\) denotes signum function of \(x\). Then \(f\) isTS EAMCET 2025 Medium
- If \(A\) and \(B\) are two independent events such that \(P(B)=\frac{2}{7}, P\left(A \cup B^c\right)=0.8\), then \(P(A)\) is equal to :TS EAMCET 2006 Medium
- \(\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}\) equalsTS EAMCET 2009 Medium
More PYQs from TS EAMCET
- If \(\sqrt{2} \sin ^2 x+(3 \sqrt{2}+1) \sin x+3>0\) and \(x^2-7 x+10 < 0\), then \(x\) lies in the intervalTS EAMCET 2019 Easy
- \(f:[2,10] \rightarrow R\) is defined as \[ f(x)=\left\{\begin{array}{cc} \frac{1}{2}(x-6)^2-3, & x \leq 4 \ x-5, & x>4 \end{array}\right. \] Which of the following is true?TS EAMCET 2021 Easy
- The polars of with respect to the two circles and areTS EAMCET 2021 Medium
- Which one of the following elements on doping with germanium, make it a p-type semiconductor?TS EAMCET 2014 Easy
- Identify \(B\) in the following reaction \(\mathrm{H}_4 \mathrm{SiO}_4 \underset{-\mathrm{H}_2 \mathrm{O}}{\stackrel{1000{ }^{\circ} \mathrm{C}}{\longrightarrow}} A \underset{\Delta}{\stackrel{\text { Carbon }}{\longrightarrow}} B+\mathrm{CO}\)TS EAMCET 2008 Hard
- If the difference in the frequencies of the first and second lines of Lyman series of hydrogen atom is \(f\), then the difference in frequencies of the first and second lines of Balmer series of hydrogen atom isTS EAMCET 2025 Medium