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

NDA 2019 · Mathematics · Continuity and Differentiability

For what value of k is the function f(x)=\ array ccc 2 x+(1)/(4) &...

For what value of kk is the function f(x)=\left\{2x+14,x<0k,x=0 continuous? (x+12)2,x>0\begin{array}{ccc} 2 x+\frac{1}{4} & , & x < 0 \\ k & , & x=0 \text{ continuous? } \\ \left(x+\frac{1}{2}\right)^2 & , & x > 0 \end{array}\right.

Options

  1. A14\frac{1}{4}
  2. B12\frac{1}{2}
  3. C1
  4. D2

Correct answer

A. 14\frac{1}{4}

Step-by-step solution

f(x)=\left\{2x+14;x<0k;x=0(x+12)2;x>0\begin{array}{cc}2 x+\frac{1}{4} & ; \quad x < 0 \\ k & ; x=0 \\ \left(x+\frac{1}{2}\right)^2 & ; \quad x > 0\end{array}\right. at x=0x=0, LHL=14\mathrm{LHL}=\frac{1}{4} and RHL=14∴\mathrm{RHL}=\frac{1}{4}\therefore Function is continous at x=0∴k=14x=0\therefore \quad k=\frac{1}{4}
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