Question

What is the limit of `(2-sqrt(x))/(4-x)` as `x` approaches 4?

Answer 1

A direct substitution results in the indeterminate form of `0/0` so we resort to L'hospital rule which states that we take the derivative of the numerator and then the denominator and then attempt to apply the limit again.

derivative of the numerator = `-1/(2sqrt(x))`

derivative of the denominator = -1

`lim_(x->4) (2-sqrt(x))/(4-x)=lim_(x->4) (-1/(2sqrt(x)))/(-1)=lim_(x->4) 1/(2sqrt(x))=1/(2sqrt(4))=1/(2*2)=1/4=0.25`