Plez help me! (limits)

1. Sep 24, 2006

jessyca_lynne

let g(x)= (x-3)sin(1/(x-3))+2. Determin ethe limit by any means possible as x-->3.

let r(x)=2+((sinx)/x)
find the limit of r(x) as x aproaches infinity

make a conjecture about the limit of r(x) as x approaches zero. give evidence to support your conjecture.

2. Sep 24, 2006

Data

What have you done so far?

3. Sep 24, 2006

jessyca_lynne

i dont know where to begin!

4. Sep 24, 2006

I suggest you use $$lim_{x\rightarrow a}(F(x)\cdot G(x))=lim_{x\rightarrow a} F(x) \cdot lim_{x\rightarrow a}G(x)$$.

5. Sep 24, 2006

Data

Well, do you know the definition of what it means to say

$$\lim_{x \rightarrow a} f(x) = L,$$

or

$$\lim_{x \rightarrow \infty} f(x) = L$$

?

Last edited: Sep 24, 2006
6. Sep 24, 2006

Data

This only works if both limits exist!

Last edited: Sep 24, 2006