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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2021 · Mathematics · Continuity and Differentiability

Consider the following statements in respect of the function f(x)=...

Consider the following statements in respect of the function f(x)=sin⁡(1x2),x≠0f(x)=\sin \left(\frac{1}{x^2}\right), x \neq 0 1. It is continuous at x=0x=0, if f(0)=0f(0)=0. 2. It is continuous at x=2πx=\frac{2}{\sqrt{\pi}}. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

f(x)=sin⁡(1x2)⇒f(x)=\sin \left(\frac{1}{x^2}\right) \Rightarrow At x=0x=0, function is undefined. ∴\therefore It is not continuous at x=0\rightarrow f(x)=\left\{sin⁡(1x2),x>0sin⁡(1x2),x<0\begin{array}{l}\sin \left(\frac{1}{x^2}\right), x > 0 \\ \sin \left(\frac{1}{x^2}\right), x < 0\end{array}\right. At x=2πx=\frac{2}{\sqrt{\pi}}, ∴f(x)\therefore f(x) is continuous at x=2πx=\frac{2}{\sqrt{\pi}}
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