#lim_(xto4)(3-sqrt(5+x))/(1-sqrt(5-x))# what will be the answer?

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Answer 1 · 2018-02-20T15:31:12

#-1/3#

#lim x->4 (3-sqrt(5+x))/(1-sqrt(5-x))#

The limit has #0/0# uncertainty. After multiplying both sides with conjugates of denominator and numerator,

#lim x->4 [(3-sqrt(5+x))(3+sqrt(5+x))(1+sqrt(5-x))]/[(1-sqrt(5-x))(3+sqrt(5+x))(1+sqrt(5-x))]#

=#lim x->4 ([3^2-(5+x)](1+sqrt(5-x)))/([1^2-(5-x)](3+sqrt(5+x)))#

=#lim x->4 ((4-x)(1+sqrt(5-x)))/((x-4)(3+sqrt(5+x)))#

=#lim x->4 (-(x-4)(1+sqrt(5-x)))/((x-4)(3+sqrt(5+x)))#

=#lim x->4 -(1+sqrt(5-x))/(3+sqrt(5+x))#

=#-2/6#

=#-1/3#