What is the limit of (2-sqrt(x))/(4-x)2x4x as xx approaches 4?

1 Answer
Oct 18, 2014

A direct substitution results in the indeterminate form of 0/000 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))12x

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