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 Jun15 comment Evaluting: $\int\frac{1}{(1+\tan x)^2} dx$ @experimentX $$\frac{\sin x}{ \sin x + \cos x} - \frac{-\cos x}{\sin x + \cos x} = 1 \neq 2$$ ;) Jun15 answered Evaluating $\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\exp(n x-\frac{x^2}{2}) \sin(2 \pi x)dx$ Jun15 awarded Enthusiast Jun13 comment Inequality between volume and its projections @nikita2 even obvious facts need a proof in mathematics :) Jun13 comment Inequality between volume and its projections @Potato sure it should be measurable. Jun13 awarded Scholar Jun13 accepted Inequality between volume and its projections Jun13 awarded Student Jun13 asked Inequality between volume and its projections Jun12 comment Do improper integrals like $\int_{-\infty}^{+\infty} f$ converge if $xf(x)\rightarrow 0$? In general the function you're integrating can have no limit at infinity. The same holds for $x f$. Take for example comb function d.pr/i/ElNd+ or if you want to deal with formulas, take sth like $f(x) = x^2 \exp (-x^8 \sin^2 (40x))$. Jun12 awarded Critic Jun12 comment Limit finding of an indeterminate form @Gigili just a typo :) Jun12 revised Limit finding of an indeterminate form edited body Jun12 comment Limit finding of an indeterminate form @AlexChamberlain take for example: $\lim_{x\to 0} \frac{\sin x}{x}$. When you're applying l'Hopital's rule, you're using the fact that $(\sin x)' = \cos x$ but it's the consequence of $\frac{\sin x}{x} \to 1$ when $x\to 0$. Jun12 answered Limit finding of an indeterminate form Jun10 awarded Commentator Jun10 comment Evaluate $\lim_{x \to \infty} \frac{1}{x} \int_x^{4x} \cos\left(\frac{1}{t}\right) \mbox {d}t$ @stariz77 btw by using $3x \cos \frac{1}{c}$ you can also determine that symbol for $f$ is $\infty$ :) Jun10 comment Evaluate $\lim_{x \to \infty} \frac{1}{x} \int_x^{4x} \cos\left(\frac{1}{t}\right) \mbox {d}t$ In general we have: $$f'(c) = \frac{f(b) - f(a)}{b-a}$$ for some $c \in (a,b)$ if a