Question

How do you find the limit `lim_(x->2^+)sqrt(2-x)` ?

Answer 1

`x\to 2^+` means that `x` is approaching 2 from the right, that is, `x>2`. But if `x>2` then `2-x<0` so that `2-x` is not in the domain of the square root function...So `\lim_{x\to 2^+}\sqrt(2-x)` does not exist , while from the left:
`\lim_{x\to 2^-}\sqrt(2-x)=sqrt(0)=0`