Question

How do you find `lim (x+1)^(3/2)-x^(3/2)` as `x->1^+`?

Answer 1

`2 sqrt 2 - 1`

Explanation:

`lim_(x to 1^+) (x+1)^(3/2)-x^(3/2)`

The function is continuous through x = 1 so you can just plug in the value x = 1 to get `2^(3/2) - 1 = sqrt 8 -1`