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.

Quote:

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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.

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I have no idea what this says.

What part or all of it?

Quote:

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Originally Posted by Mathsnewbie

What part or all of it?

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The vast majority of it.

Quote:

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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.

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Have you read what you wrote?