tell if the function is continuous at x2 x22Solutionfor this

tell if the function is continuous at x=2 (x^2-2)

Solution

for this function to be continuos we only need to prove that x^2 is continuous.

The product of continuous functions is continuous. The function \'x\' is continuous, hence also x2=xx=x^2 is continuous.

The proof that the product of continuos functions is continuous, simply relies on the theorem that states the limit of the product is the product of the limits.