Calculus & Analysis Marathon & Questions (1 Viewer)

porcupinetree

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Calculus & Analysis Marathon & Questions
This is a marathon thread for single-variable calculus & analysis (mainly real and maybe complex analysis). Please aim to pitch your questions for first-year/second-year university level maths. Excelling & gifted/talented secondary school students are also invited to contribute.

(mod edit 7/6/17 by dan964)

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Thought it'd be a good idea to start a marathon for users to post and answer first year uni calculus problems.

First question:

 
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leehuan

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Re: First Year Uni Calculus Marathon

I can't word properly yet.









 
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Trebla

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Re: First Year Uni Calculus Marathon

lel these look like tute or lecture qns

(I actually remember the above question haha)
 

leehuan

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Re: First Year Uni Calculus Marathon












=======================




 
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InteGrand

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Re: First Year Uni Calculus Marathon

Is this thread's main intention as a Q&A, or as a challenge thread?
 

leehuan

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Re: First Year Uni Calculus Marathon

Is this thread's main intention as a Q&A, or as a challenge thread?
I think exercise/challenge

My cries for help are going to remain in seperate threads
 

seanieg89

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Re: First Year Uni Calculus Marathon

(A bit tricky)

For which positive integers k is it possible to find a continuous function f:R->R that such that

f(x)=y

has exactly k solutions x for every real number y?
 

leehuan

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Re: First Year Uni Calculus Marathon

(A bit tricky)

For which positive integers k is it possible to find a continuous function f:R->R that such that

f(x)=y

has exactly k solutions x for every real number y?
Is there any answer besides k=1?
 

seanieg89

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Re: First Year Uni Calculus Marathon

Is there any answer besides k=1?
Indeed that is the essence of the question, I don't want to spoil it too quickly. It is very good exercise to reach a conclusion yourself and try to rigorously justify it. (The main tools at your disposal being properties of continuous functions like the intermediate and extreme value theorem).
 

porcupinetree

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Re: First Year Uni Calculus Marathon

lel these look like tute or lecture qns

(I actually remember the above question haha)
There was a tute question similar to that question, with x^2 instead of x^3. (But it's the same general process.)

Is this thread's main intention as a Q&A, or as a challenge thread?
Challenge/exercise, just like the other maths marathons
 

leehuan

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Re: First Year Uni Calculus Marathon


















I hope...
 

leehuan

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Re: First Year Uni Calculus Marathon



For completeness sake
 

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