Question

The value of $k$ so that the function $f(x) = \begin{cases} \frac{x^{4}-256}{x-4}, & \text{if $x \neq 4$ } \\[2ex] k, & \text{if $x=4$ } \end{cases}$
is continuous at $x = 4$ is

• A. 128
• B. 64
• C. 256
• D. None of these

Answer 1

Answer: (C)

$f(x)$ is continuous at $x=4$
$\Rightarrow f(4)=\displaystyle\lim _{x \rightarrow 4} \frac{x^{4}-256}{x-4}$
$=\displaystyle\lim _{x \rightarrow 4} \frac{x^{4}-4^{4}}{x-4}=4 \cdot 4^{4-1}=256$