limit x-> 4 x^2+k^2 over x-4

Question

learning limit

Answer 1

(x²+k²)/(x-4)=(x+4)+(k²+16)/(x-4) using algebraic long division.

Limit as x→4 of the expanded expression makes (k²+16)/(x-4) infinite, while x+4→4. So the limit of the original expression is also infinite as x→4.