Finding the Limit of g(x) and r(x) as x Approaches a Specific Value

[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.

 

[Data]

What have you done so far?

 

[jessyca_lynne]

i don't know where to begin!

 

[radou]

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.

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

 

[Data]

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

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

or

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

?

 

[Data]

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

This only works if both limits exist!