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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2023 · Mathematics · Continuity and Differentiability

Let f(x)=\ array cl (x-3)/(|x-3|)+a ; & x 3 array .f(x) be...

Let f(x)=\left\{x−3∣x−3∣+a;x<3a−b;x=3 and x−3∣x−3∣+b;x>3\begin{array}{cl}\frac{x-3}{|x-3|}+a ; & x < 3 \\ a-b ; & x=3 \text{ and } \\ \frac{x-3}{|x-3|}+b ; & x > 3\end{array}\right.f(x) be continuous at x=3x=3. What is the value of b?

Options

  1. A-1
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

⇒−1+\Rightarrow-1+\mathrm{a}=\mathrm{a}−b⇒b=1-\mathrm{b} \Rightarrow \mathrm{b}=1
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