What is the limit where lim_(x → 1) (sqrt(3+x)-sqrt(5-x))/(x^2-1)?

(sqrt(3+x)-sqrt(5-x))/(x^2-1)

1 Answer
Apr 5, 2018

1/4.

Explanation:

"The Reqd. Lim."=lim_(x to 1){sqrt(3+x)-sqrt(5-x)}/(x^2-1),

=lim{sqrt(3+x)-sqrt(5-x)}/(x^2-1)xx{sqrt(3+x)+sqrt(5-x)}/{sqrt(3+x)+sqrt(5-x)},

=lim{(3+x)-(5-x)}/{(x^2-1)(sqrt(3+x)+sqrt(5-x))},

=lim{2cancel((x-1))}/{cancel((x-1))(x+1)(sqrt(3+x)+sqrt(5-x))},

=lim_(x to 1)2/{(x+1)(sqrt(3+x)+sqrt(5-x))},

=2/{(1+1)(sqrt(3+1)+sqrt(5-1)).

rArr "The Reqd. Lim."=1/4.