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

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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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