# Solving limits algebraically

1. Aug 3, 2010

### sixstring91

1. The problem statement, all variables and given/known data

Just brushing up on my calculus before I start college, but I'm having difficulty manipulating two different limit equations algebraically (sorry I can't find out how to put these into latex):

1) lim (t->0) {1/[t*sqrt(1+t)]} - (1/t)

2) lim (x->-4) [sqrt(x^2+9) - 5]/(x+4)

3. The attempt at a solution

don't know where to begin on (2), but for (1):

mult (1/t) by sqrt(1+t) to match denominators, left with [1 - sqrt(1+t)]/[t*sqrt(1+t)]

any hints?

2. Aug 3, 2010

### Dick

Try multiplying the numerator and denominator by 1+sqrt(1+t). Expand out the numerator and see what happens.

3. Aug 3, 2010

### Bohrok

For 2), multiply the numerator and denominator by the conjugate of the numerator.

4. Aug 3, 2010

### sixstring91

Ah, both of you were spot on with the conjugates. Thanks for your help.