Question

If $f(x)\left{ \begin{matrix}

• 1, & x & \begin{matrix} < & 0 \end{matrix} \ 0, & x & \begin{matrix} = & 0 \end{matrix} \ 1, & x & \begin{matrix}

& 0 \end{matrix} \end{matrix} \right.\ $then in order that f be continuous at$x + \frac{1}{x}$, the value of c is

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (C)

6

Answer 2

$\lim _ { x \rightarrow 0 + } f ( x ) = \lim _ { x \rightarrow 0 + } \frac { x ^ { 2 } + 2 x + c } { 1 - 3 x ^ { 2 } } = \frac { c } { 1 } = c$

Hence for $f$to be continuous c = 6.