Limit Questions: Finding Solutions for Limits Problems

[powp]

can anybody help me with these two question for finding limits:

1. lim h -> 0 ((3+h)^-1 - 3^-1)/h
2. lim x -> -4- |x+4|/x+4


please help

 

[shmoe]

1. looks an awful lot like the kind of limit you find in the definition of the derivative. If you haven't seen derivatives yet (or even if you have) try finding a common demoninator to simplify (3+h)^(-1) - 3^(-1)

2.you're interested in values of x that are less than -4. Use this to simplify the absolute value.

 

[powp]

for number one if I make it so that I only have positive exponents and simplify I end up with

1 /(9 + 3h) now if I plug in 0 the result is 1 / 9. Is this correct?

 

[Math Is Hard]

I think you might have a sign error. Check this step in the numerator and tell me what you think:
(3-(3+h))/(9 + 3h) should distribute as (3-3-h)/(9 + 3h) or -h/(9 +3h)

 

[powp]

yeah it looks like I did make an error should be -1/9? right?

 

[Math Is Hard]

That's what I got, but maybe one of the local mathletes will stop by and verify.