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am100181

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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