Evaluate the following limits lim x tends to 0[√3+x – √5-x]/x^2–1?

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Answer 1 · 2018-02-23T03:45:08

sqrt(5)-sqrt(3)

We have:

#Lim_(x->0)[sqrt(3+x)-sqrt(5-x)]/(x^2-1)#

Let's first try plugging in #x=0# to see if further simplification or manipulation is even necessary:

#(sqrt(3+0)-sqrt(5-0))/(0^2-1)#

We don't have an indeterminate form, so, we can continue to simplify, and this will be our limit:

#(sqrt(3)-sqrt(5))/-1#

#-(sqrt(3)-sqrt(5))=sqrt(5)-sqrt(3)#