# flapjackery

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# 86 Questions

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### Sequence of $f_n \in R[0, 1]$ that converges pointwise to $f \in R[0, 1]$ such that $\lim_{n \to \infty} \int_0^1 f_n dx \neq \int_0^1 f dx$.

1d ago Raff 26.2k

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### For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge?

nov 20 at 4:35 flapjackery 719

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### Find all possible linear fractional transformations that map circles $|z-1|=1$ and $|z+1|=1$ onto lines $Re(w)=1$ and $Re(w)=-1$ and $z=2$ to $w=1$.

nov 17 at 18:40 flapjackery 719

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### Using complex analysis, calculate $I_m = \int_{-\infty}^\infty \frac{dx}{1+x+x^2+\cdots+x^{2m}}$ for $I_2$ and $I_3$

nov 13 at 5:41 flapjackery 719

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### $f:[0,1] \to \mathbb{R}$ with $f(0) = 0 = f(1)$ and $|f''|\leq M$. Show $|f'(1/2)| \leq \frac{M}{4}$. [duplicate]

nov 11 at 5:39 flapjackery 719

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### $f: \mathbb{R} \to \mathbb{R}$ and $f(x)>0$ $\forall x \in \mathbb{R}$. Prove $\exists \epsilon >0: f(x) > \epsilon$ for all $x \in [-10,10]$

nov 1 at 4:44 flapjackery 719

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