# Mann

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 15 Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$ 10 What's the formula to solve summation of logarithms? 7 Finding the derivative of $y^x = e^y$ 7 Does $\sum _{ n=1 }^{ \infty }{ \frac { 1 }{ n } }$ diverge? 7 how do I prove that $1 > 0$ in an ordered field?

# 3,374 Reputation

 +10 Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$ +10 Counterexample to conjecture (beginner) +10 what is the$\int \sin (x^2) \, dx$? +10 Direct Irrationality Proof for $\sqrt{3}$ and $\sqrt{6}$

# 203 Questions

 10 Reflections on math education 10 Number theory fun problem 7 Consider $f_n(x) = \sum_{k=0}^{n} {x^k}$. Does $f_n$ converge pointwise on $[0,1]$? 7 Must the (continuous) image of a null set be null? 7 Is a homeomorphism which maps lines to lines (and fixes zero) necessarily linear?

# 102 Tags

 105 calculus × 130 22 real-analysis × 92 55 homework × 78 22 integration × 25 39 sequences-and-series × 20 20 logarithms × 5 27 algebra-precalculus × 19 16 number-theory × 9 24 trigonometry × 15 15 inequality × 16

# 2 Accounts

 Mathematics 3,374 rep 1530 Skeptics 101 rep 1

 +50 if derivative vanishes in a path connected set, then $f$ is constant on that set? +50 Derivative of sum of two functions is the sum of their derivatives. +50 Locally compactness of euclidean space