Question

The value of k so that the function
$f\left(x\right)=\{\begin{array}{ccc}k(2x-x^2),& when& x<0\\ cosx,& when& x\ge 0\end{array}$ is continuous at x = 0, is

• A. 1
• B. 2
• C. 4
• D. None of these

Answer 1

The correct option is D None of these

$f(0-)={lim}_{x\to 0-}k(2x-x^2)=0;f(0+)={lim}_{x\to 0+}cosx=1$
$\therefore f\left(0\right)=cosx=1$
Hence no value of k can make f(0-) = 1