Find the limit as x approaches 1 for the equation: (x^2 +1)/(sqrt(2x+2) -2)?

Question

Find the limit as x approaches 1 for the equation: (x^2 +1)/(sqrt(2x+2) -2)?

Answer 1

is it supposed to be x^2 - 1 on top? the way you have it now, the limit does not exist beacuse you'll get 2/0 if you plug in 1. If you had the indeterminate form 0/0 then you have some work to do

Answer 2

Infinity.

The denominator approaches zero as x approaches 1:

sqrt(2*1 + 2) = sqrt (4) = 2

.. therefore, 2-2 = 0, the denominator approaches 0.

Anything divided by 0 = Infinity.

Therefore, this equation tends to positive infinity as x tends to 1.

Answer 3

As you've written it, it doesn't exist.

Did you mean this (note the subtraction in the numerator)?

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