Let g(x)= cases px+9 -3 x ,& x 0 ,& x=0 cases

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let

g(x)=\begin{cases}\dfrac{\sqrt{px+9}-3}{x},& x\neq 0\\k,& x=0\end{cases}.

Determine the real numbers

p

and

k

that satisfy the following conditions: (i)

g(x)

is continuous at

x=0

. (ii)

k=g(1)