Manipulating Limits Algebraically: Solving Tricky Equations

[sixstring91]

Homework Statement

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)

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?

 

[Dick]

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

 

[Bohrok]

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

 

[sixstring91]

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

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

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