a) Suppose f:R → R is differentiable on R. Prove that if f ' is bounded...

a) Suppose f:R → R is differentiable on R. Prove that if f ' is bounded on R then f is uniformly continuous on R.
b) Show that g(x) = (sin(x⁴))/(1 + x²) is uniformly continuous on R.
c) Show that the derivative g'(x) is not bounded on R.

Expert Solution

Colby Messinger answered 2 years ago

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