# Limits

• Mar 3rd 2010, 11:19 AM
Mathsnewbie
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.
• Mar 3rd 2010, 12:13 PM
Drexel28
Quote:

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.
• Mar 3rd 2010, 01:16 PM
Mathsnewbie
What part or all of it?
• Mar 3rd 2010, 01:32 PM
Drexel28
Quote:

Originally Posted by Mathsnewbie
What part or all of it?

The vast majority of it.
• Mar 3rd 2010, 06:21 PM
Diego
Quote:

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?