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 47 Is differentiating on both sides of an equation allowed? 5 Prove that $f$ has a fixed point. 3 Is there any closed form solution for a function $f$ on $\mathbb R$ satisfying $f(t+s)=f(t)f(s)$ 2 Show that $X^3+X^2+1$ has only one real root 2 The composition of a nowhere-differentiable function with a differentiable function.

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 6 Evaluate $\int_0^\infty \frac{\sqrt{x}}{x^2+1}\log\left(\frac{x+1}{2\sqrt{x}}\right)\;dx$ 1 Evaluating Certain $L$-functions

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 52 calculus × 3 2 abstract-algebra 6 functions × 3 2 function-and-relation-composition 6 real-analysis × 2 2 examples-counterexamples 2 elementary-number-theory × 2 2 derivatives 2 polynomials 1 prime-numbers

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