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Help with multivariate Calculus

  • Thread starter am100181
  • Start date
  • #1
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Homework Statement



Show that:

max{a,b}=1/2*(a+b+|a-b|)

Hence or otherwise, show that if f,g:R ----> R are continuous, then the function h:R ----> R defined by h(x) = max{f(x),g(x)}
is also continuos.

Suppose the f:(0,inf) ---> R is differentiable and f(x) ---> 0 as x---> inf. Set g(x) = f(x+1-f(x). Prove that g(x) ---->0 and x----> inf.


The Attempt at a Solution



How do I start attempting such questions? I am thinking of taking multivariate next sem and am wanting to prepare myself for such questions....

Thank you
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Welcome to PF!

Show that:

max{a,b}=1/2*(a+b+|a-b|)

How do I start attempting such questions?
Hi am100181! Welcome to PF! :wink:

Just treat the two cases a≥ b and a< b separately. :smile:
 

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