Category: Differentiation

Question Number 143505 by mim24 last updated on 15/Jun/21 Commented by mr W last updated on 15/Jun/21 $$f\left(x\right)=\frac{x}{(x+2+\sqrt{3})(x+2-\sqrt{3})}$$$$f\left(x\right)\to \pm \mathrm{\infty }whenx\to -2\pm \sqrt{3}$$$$\Rightarrow nomaximum,nominimum$$ Answered…

Question Number 143461 by Willson last updated on 14/Jun/21 $$\mathrm{Prove}\mathrm{that}:\mathrm{\forall }\mathrm{n}\in {\mathbb{N}}^{\ast }$$$$\mathrm{a}.\underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}{C}_{\mathrm{n}}^{\mathrm{k}}\frac{{(-1)}^{\mathrm{k}}}{\mathrm{k}}=\underset{\mathrm{k}=1}{\sum ^{\mathrm{n}}}\frac{1}{\mathrm{k}}$$$$\mathrm{b}.\:\:\:\:\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}{C}_{\mathrm{n}} ^{\mathrm{k}} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{k}}…

Question Number 143429 by mnjuly1970 last updated on 14/Jun/21 $$$$$$\dots \dots .nice\dots ..integral\dots \dots .$$$$Evaluate::$$$$\xi :={\int }_0^1\frac{ln(1-t)}{1+t^2}dt=?$$ Answered by Dwaipayan Shikari…

Question Number 12275 by @ANTARES_VY last updated on 17/Apr/17 $$\oint \left(\mathbf{x}\right)=\frac{\mathbf{x}}{1-\mathbf{x}}.{\oint }^{\prime }\left(2\right)=?.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 143231 by mnjuly1970 last updated on 11/Jun/21 $$\dots ..mathematical\dots \dots Analysis\dots .$$$$if::\mathit{\varphi }\left(n\right):={\int }_0^1{x}^{2n-1}log(1+x)dx$$$$thenfindthevalueof::$$$$\mathrm{\Theta }:=\underset{n=1}{\sum ^{\mathrm{\infty }}}{(-1)}^n\mathit{\varphi }\left(n\right)$$$$\:\:\:\:\:\:…….{m}.{n} \…