[Solution] Let f(x)= sin (e^x), f : R → R. Prove that there is a function g : R → R such that g ’ (x) = f(x), for each x Є R. Prove that any such function
Question: Let \(f\left( x \right)=\sin \left( {{e}^{x}} \right)\), f : R → R.
- Prove that there is a function g : R → R such that g ’ (x) = f(x), for each x Є R.
- Prove that any such function g is continuous.
- Prove that, if h : R →R is another such function, then h differs from g by a constant.
- Prove that any such function is monotone on (-∞; 0], but not on [0;∞).
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