Help with multivariate Calculus

[am100181]

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

 

[tiny-tim]

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!

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