Question

Find the value of k that makes f(x) continuous at x = 4

Answer 1

Given:

The function is continuous at x = 4,

`f(x)=\begin{cases}(2x^2-8x)/(x-4),x\\e4 \\ k\text{ ,x= 4}\end{cases}`

As the given function is continous at x = 4,

`\begin{gathered} \lim _(x\to4)f(x)=k \\ \lim _(x\to4)((2x^2-8x)/(x-4))=k \\ \lim _(x\to4)((2x(x-4))/(x-4))=k \\ \lim _(x\to4)(2x)=k \\ 2(4)=k \\ k=8 \end{gathered}`

Answer: k = 8