# Math Help - Limits

1. ## Limits

Hey guys I have a few questions I can't do on limits. They are

i) Consider the functions f(-1,Pie) implies R whose graph y=f(x) is given by - here there's a graph which says y=sin(x) and y=x-x^3 just one line though.

Prove that the lim f(x)/x as x implies 0 exists.

I know how to do limits for normal functions like if it was Cos(x) it would tend to 1 and x tended to 0 but don't know how to do this.

ii) State the definition of Inf(A) and Lim(A) and prove that if lim f(x)=L as x tends to 0 and lim g(x) = M as x tends to 0 then lim(f(x)+g(x))=L+M.

Don't even know how to start this part to be honest.

2. Originally Posted by Mathsnewbie
Hey guys I have a few questions I can't do on limits. They are

i) Consider the functions f(-1,Pie) implies R whose graph y=f(x) is given by - here there's a graph which says y=sin(x) and y=x-x^3 just one line though.

Prove that the lim f(x)/x as x implies 0 exists.

I know how to do limits for normal functions like if it was Cos(x) it would tend to 1 and x tended to 0 but don't know how to do this.

ii) State the definition of Inf(A) and Lim(A) and prove that if lim f(x)=L as x tends to 0 and lim g(x) = M as x tends to 0 then lim(f(x)+g(x))=L+M.

Don't even know how to start this part to be honest.
I have no idea what this says.

3. What part or all of it?

4. Originally Posted by Mathsnewbie
What part or all of it?
The vast majority of it.

5. Originally Posted by Mathsnewbie
Hey guys I have a few questions I can't do on limits. They are

i) Consider the functions f(-1,Pie) implies R whose graph y=f(x) is given by - here there's a graph which says y=sin(x) and y=x-x^3 just one line though.

Prove that the lim f(x)/x as x implies 0 exists.

I know how to do limits for normal functions like if it was Cos(x) it would tend to 1 and x tended to 0 but don't know how to do this.

ii) State the definition of Inf(A) and Lim(A) and prove that if lim f(x)=L as x tends to 0 and lim g(x) = M as x tends to 0 then lim(f(x)+g(x))=L+M.

Don't even know how to start this part to be honest.
Have you read what you wrote?