The function is defined by f(x)= cases kx^ 2 +3, & x=1

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

Problem

The function

f

is defined by

f(x)=\begin{cases} kx^{2}+3, & x=1,\\ x^{2}+3, & x\neq 1. \end{cases}

For which value of

k

f

continuous at

x=1

, and what is

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

? (a)

k=4,\;\lim =4

(b)

k=1,\;\lim =3

(c)

k=1,\;\lim =4

(d)

k=0,\;\lim =3