Question

How do you find the limit of `sqrt(2-x^2)/(x+1)` as `x->0^+`?

Answer 1

Substitution.

Explanation:

As `xrarr0`, the denominator does not go to `0`, so we can use substitution to see that

`lim_(xrarr0^+)sqrt(2-x^2)/(x+1) = sqrt(2-(0)^2)/((0)+1) = sqrt2`