QuestionFind the value of $k$ such that $\lim _{x \rightarrow 2} f(x)=3$ for $f(x)=\frac{(x-2)(x^{2}-k^{2})}{(x^{2}-4)(x-k)}$.

Studdy Solution
olving the equation for $k$ gives us$$3 = \frac{2+k}{4}$$$$3 \times4 =2 + k$$$$12 =2 + k$$$$k =12 -2$$$$k =10$$So, the value of $k$ that makes $\lim{x \rightarrow2} f(x)=3$ is $10$.
The correct answer is (C)10.