Question

Find the value of k that makes f(x) continuous at x = 3

Answer 1

Given:

The function is,

`f(x)=f(x)=\begin{cases}(x-3)/(x^2+2x-15),x\\e3 \\ k,x=3\end{cases}`

As the given function is continous at x= 3 ,

`\begin{gathered} \lim _(x\to3)f(x)=k \\ \lim _(x\to3)((x-3)/(x^2+2x-15))=k \end{gathered}`