# Xiaolang

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 2 Determining Volume by rotation of a plane 2 Real analysis - converging sequence 2 Solving the improper integral $\int_0^{\infty} {e^{-ax}\cos{(bx)}} dx$ 2 How to find $\int \frac{2x}{x^4+1}dx$ 2 Choosing teams with minimum number of boys and girls.

# 212 Reputation

 +60 Which harmonic numbers have prime numerators? +8 Proving that $\sum_{k=0}^{n} {{m+k} \choose{m}} = { m+n+1 \choose m+1 }$ +10 Using the Limit definition to find the derivative of $e^x$ +10 How to prove a convergence of a Taylor series to $f$

# 7 Questions

 12 Which harmonic numbers have prime numerators? 7 How to prove these integral inequalities? 2 How prove the integral inequality 0 An integral inequality $\frac1{b-a} \int_a^b e^{f(x)}dx\ge e^{\frac1{b-a} \int_a^bf(x)dx}$ 0 True of False :A liner combination of (root irrational number) $a^b$ $(a \in Q_+ b \in Q)$ is a irrational number?

# 22 Tags

 9 calculus × 13 2 limits × 3 7 integration × 4 2 sequences-and-series × 2 4 improper-integrals × 2 2 convergence × 2 3 real-analysis × 6 2 indefinite-integrals 3 combinatorics × 2 2 multivariable-calculus

# 1 Account

 Mathematics 212 rep 110