Question

So confused:( please help!!!!
If possible, choose k so that the following function is continuous on any interval:
f(x)=(6x^5−18x^4)/x−3
f(x)=k
x≠3
x=3.

Answer 1

So the first f is for when we have x is not equal to 3 and the second f is for when we have x=3, I'm assuming.

Find the left and right limit as x approaches 3.
But from the right of 3 and left 3, we have the same function so just find the limit as x approaches 3 of f.
Then find f(3) which is k since f(x)=k for when x=3.
So you have the following equation to solve for k:
\[f(3)=\lim_{x \rightarrow 3}f(x) => k=\lim_{x \rightarrow 3}f(x)\]

Answer 2

find that limit part and that will be k.