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  3. only need to solve 5 write clearly and show which...

Question: only need to solve 5 write clearly and show which...

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Only need to solve 5. write clearly and show which concepts used for a thumbs up

Exercise 3. Show that if f : R → R is twice differentiable on R, then f is convex if and only if f20 on R. Exercise 4. Let f : (0, oo) → R be differentiable on (0,oo) with f,(z) → 0 as x → οο Determine the limit of f(x +1)- f(x) as o Exercise 5. Let g : R -R be differentiable on R with a bounded derivative g: R - R. Prove that f : R R given by f(x)-x + єд(x) is bijective if e> 0 is small enough.

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