## Answers

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Lim √x2 + x - √x

x->∞

let x=1/y so that y->0, when x->∞

Lim √1/y2 + 1/y - √1/y

y->0

Lim 1/y + 1/y - √1/y

y->0

Lim (1+1)/y - √1/y

y->0

Lim 2/y - √1/y

y->0

Lim 2/y - 1/√y

y->0

Lim (2√y - y)/y√y

y->0

Lim (2√y - y)/y√y x (2√y + y)/(2√y + y)

y->0

Lim (4y - y2)/y√y(2√y + y)

y->0

Lim (4y - y2)/(2y2 + y2√y)

y->0

dividing each term with the highest power of y

Lim (4y/y2 - y2/y2)/(2y2/y2 + y2√y/y2)

y->0

Lim (4/y - 1)/(2 + √y)

y->0

(4/0 - 1)/(2 + 0)

0 - 1 / 2

x->∞

let x=1/y so that y->0, when x->∞

Lim √1/y2 + 1/y - √1/y

y->0

Lim 1/y + 1/y - √1/y

y->0

Lim (1+1)/y - √1/y

y->0

Lim 2/y - √1/y

y->0

Lim 2/y - 1/√y

y->0

Lim (2√y - y)/y√y

y->0

Lim (2√y - y)/y√y x (2√y + y)/(2√y + y)

y->0

Lim (4y - y2)/y√y(2√y + y)

y->0

Lim (4y - y2)/(2y2 + y2√y)

y->0

dividing each term with the highest power of y

Lim (4y/y2 - y2/y2)/(2y2/y2 + y2√y/y2)

y->0

Lim (4/y - 1)/(2 + √y)

y->0

(4/0 - 1)/(2 + 0)

0 - 1 / 2

**-1/2**it is the answer....### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

The given question is not clearly specified.

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x->∞