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

1 Answer
AJ Speller
Oct 18, 2014

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

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