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Year 12s: what will be the first way you research your future options? >>

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Year 12s: what will be the first way you research your future options? >>

Students on campus at the University of Warwick

University of Warwick

Coventry

First Year Maths Past Papers And Shizzle Brap Brap

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Hathlan

You need to show f(0)=0. Without this we don't know that

lim_{x\rightarrow0} \frac{f(0)}{g(x)}

exists, since we have the g(x) tending to zero. Otherwise good.

How does one show f(0)=0? If I am not mistaken, you mentioned that f(0)=0 by showing that lim as x tends to 0 of f(x) is zero then using continuity which is not very clear to me. :frown:

:frown:

Students on campus at the University of Warwick

University of Warwick

Coventry

OP

6DOIT

How does one show f(0)=0? If I am not mistaken, you mentioned that f(0)=0 by showing that lim as x tends to 0 of f(x) is zero then using continuity which is not very clear to me. :frown:

:frown:

It's not trivial;

Spoiler

With the January exam coming up, any other first years wanna start this thread up again?

Original post by matt2k8

With the January exam coming up, any other first years wanna start this thread up again?

I want a new thread! :h:

:h:

Original post by Hathlan

Analysis 2006

for (i) why not just

(a_n)= \sqrt(n) or \log(n)

Original post by davidcarvalho

for (i) why not just

(a_n)= \sqrt(n) or \log(n)

Neither of them are bounded - this question confused me too, emailed my supervisor about it :s-smilie:

:s-smilie:

Edit - after messing with it some more I found out

cos(\sqrt{n} \pi)

works, using the inequality

|cos a - cos b| \leq |a -b|

and the fact

(\sqrt(n+1) - \sqrt(n)) \rightarrow 0

(edited 13 years ago)

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