I have no idea how to solve it.

Update!

I just did this question:

a) 3.5

B) infinity, but I am not sure why positive infinity??? Can someone explain it to me, please?

The answers are right, I just need to find out why...

How did you "do" these if you don't know how they're done?

a) lim (as x goes to infinity) of (square root of [x^2+7+1]-x)

(I'm going to assume that the "7" is supposed to be a "7x".)

Right now, the expression is "infty - infty = 0" because sqrt{x^2} = x and the 7x and the 1 don't really matter. But that's "indeterminate". The regular way to get around this problem with addition or subtraction with roots is to do the conjugate:

The bottom doesn't divide by zero and the top isn't "0 - 0" anymore so you can take the limit. One way is to divide everything by x:

b) lim (as x goes to - infinity) of (square root of [x^2+7+1]-x)

This time (because x is negative) you have to do the absolute value part: sqrt{x^2} = |x|. Since x < 0 then |x| = -x. So you have "-x - x = -2x". Evaluate.