12 Proving $-\frac{1}{a}<\int_a^b \sin(x^2) dx<\frac{1}{a}$ 10 Bounding the absolute value of a function with an integral 8 How to check $x^2+y^2+z^2=7 w^2$ admits no no-trivial integral solution? 7 Find $\lim_{n\to\infty} a_n$ 7 How to prove the second mean value theorem for definite integrals

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 +10 Show if the function $\frac{x+2}{x^2+2x+1}$ is injective +10 Show that there is a root in [0,1] +10 Indefinite integral:$\int \cos(2018x)\sin^{2016}(x)dx$ +10 Maximize area of a quadrilateral given three sides

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 3 First Fourier coefficient of weight $k$ holomorphic cusp form.

### Tags (145)

 51 calculus × 25 26 limits × 12 47 elementary-number-theory × 27 22 sequences-and-series × 15 38 number-theory × 23 19 geometry × 19 37 real-analysis × 24 17 algebra-precalculus × 11 26 modular-arithmetic × 14 17 linear-algebra × 10

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 3 Prove that for $\forall m, n \in \mathbb Z$ such that $[7(m + n)^2 + 2mn] \ \vdots \ 225$ then $mn \ \vdots \ 225$.