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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2019 · Mathematics · Continuity and Differentiability

The value of k which makes f(x)=\ array cc x & x ≠ 0 k & x=0 array...

The value of k which makes \mathrm{f}(\mathrm{x})=\left\{sin⁡xx≠0kx=0\begin{array}{cc}\sin x & x \neq 0 \\ k & x=0\end{array}\right. continuous at x=0\mathrm{x}=0, is

Options

  1. A2
  2. B1
  3. C-1
  4. D0

Correct answer

D. 0

Step-by-step solution

f(x)=\left\{sin⁡x,x≠0k,x=0\begin{array}{cc}\sin x, & x \neq 0 \\ k, & x=0\end{array}\right. Given, f(x)f(x) is continuous at x=0x=0lim⁡x→0f(x)=f(0)⇒lim⁡x→0sin⁡x=k⇒k=0\begin{aligned} & \lim _{x \rightarrow 0} f(x)=f(0) \\ & \Rightarrow \lim _{x \rightarrow 0} \sin x=k \\ & \Rightarrow \mathrm{k}=0\end{aligned}$$
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