Let f(x)= cases x^ 2 +3,& x<1 x,& x 1 cases For which value of does exist?

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

f(x)=\begin{cases}x^{2}+3,& x<1\\k\sin x,& x\ge 1\end{cases}

For which value of

k

does

\displaystyle\lim_{x\to 1}f(x)

exist? (a)

4\sin 1

(b)

\dfrac{4}{\cos 1}

(c)

\dfrac{4}{\sin 1}

(d)

4