Verifying & Evaluating Limits

[mathxyz]

My teacher started limits this week. I am learning so much and actually think that my math journey this coming fall in calculus 1 will be great.
However, I came across 2 limit questions that really don't make sense to me.

Evaluating Limits:

1) Find the limit of (x - 4)^3/| 4 -x | as x --> 4.

NOTE: The symbol | | = absolute value.

Verifying Limits:

1) Find the limit of 3x sin(1/x) = 0 as x --> 0.

P.S. I am having trouble finding the limit of trig functions.

 

[pka]

For #1, (x-4)<SUP>3</SUP>=|x-4|<SUP>2</SUP>(x-4).
And, |x-4|=|4-x|!
Now you take it from there.

 

[mathxyz]

ok

I am NEW AT LIMITS. I need someone to walk me through slowly.
Soroban already took care of those steps.

 

[Gene]

I think for the second you have to use
-1 < sin(u) < 1 for all u
so multiply that by 3x to get
-3x < 3x*sin(1/x) < 3x as x -> 0

 

[stapel]

Weren't you already provided with the complete worked solution at one of the other places you posted this?

Eliz.