Question

PLease help!!!!!
Find a value for k in the function below so that the function is continuous at all points.
f(x)={((x^5-32)/(x-2)) , x≠2, k, x=2

k=

Answer 1

find the limit at \(x=2\) and replace \(k\) by that number

Answer 2

it might help to know that
\[x^5-32=(x-2) (x^4+2 x^3+4 x^2+8 x+16)\] so you can cancel the factor of \(x-2\) top and bottom and replace \(x\) by \(2\) in \(x^4+2 x^3+4 x^2+8 x+16\)

that will be your \(k\)