Question Number 121066 by Jamshidbek2311 last updated on 05/Nov/20 $$\left.\mathrm{1}\right)\int\frac{{x}}{{x}+\mathrm{1}}{dx}=? \\ $$$$\left.\mathrm{2}\right)\int\frac{{x}}{\:\sqrt{{x}−\mathrm{1}}}{dx}=? \\ $$$$\left.\mathrm{3}\right)\int{x}\sqrt{{x}−\mathrm{4}}{dx}=\overset{} {?} \\ $$$$ \\ $$ Commented by liberty last updated on…
Question Number 186597 by Mingma last updated on 06/Feb/23 Answered by Frix last updated on 07/Feb/23 $$\mathrm{123} \\ $$$$\mathrm{132} \\ $$$$\mathrm{213} \\ $$$$\mathrm{231} \\ $$$$\mathrm{312}…
Question Number 121014 by mathocean1 last updated on 04/Nov/20 $$\mathrm{show}\:\mathrm{by}\:\mathrm{recurrence}\:\mathrm{that} \\ $$$$\forall\:\mathrm{n}\geqslant\mathrm{1}\:, \\ $$$$\mathrm{a}^{\mathrm{n}} −\mathrm{b}^{\mathrm{n}} =\left(\mathrm{a}−\mathrm{b}\right)\left(\mathrm{a}^{\mathrm{n}−\mathrm{1}} +\mathrm{a}^{\mathrm{n}−\mathrm{2}} \ast\mathrm{b}+…+\mathrm{ab}^{\mathrm{n}−\mathrm{2}} +\mathrm{b}^{\mathrm{n}−\mathrm{1}} \right) \\ $$ Answered by mathmax…
Question Number 121012 by mathocean1 last updated on 04/Nov/20 $$\mathrm{x};\mathrm{y};\mathrm{z}\:\in\:\mathbb{N}^{\ast\:} \mathrm{with}\:\mathrm{x}>\mathrm{3}\:\mathrm{are}\: \\ $$$$\mathrm{numbers}. \\ $$$$\mathrm{we}\:\mathrm{suppose}\:\mathrm{that}\:\mathrm{y}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{121}\:\mathrm{in}\:\mathrm{base}\:\mathrm{x}\:\mathrm{and}\:\mathrm{z}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\mathrm{110}\:\mathrm{in}\:\mathrm{base}\:\mathrm{x}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{show}\:\mathrm{that}\:\mathrm{we}\:\mathrm{can}\:\mathrm{write} \\ $$$$\left(\mathrm{without}\:\mathrm{knowing}\:\mathrm{x}\right)\:\mathrm{the}\: \\ $$$$\mathrm{product}\:\mathrm{xyz}\:\mathrm{in}\:\mathrm{base}\:\mathrm{x}.…
Question Number 120847 by Jamshidbek2311 last updated on 03/Nov/20 $${If}\:{x},{y},{z}\:\:{then}\:{prove}\:{the}\:{following} \\ $$$${inequality} \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{2}\right)\left({y}^{\mathrm{2}} +\mathrm{2}\right)\left({z}^{\mathrm{2}} +\mathrm{2}\right)=\mathrm{9}\left({xy}+{yz}+{xz}\right) \\ $$ Commented by Jamshidbek2311 last updated on…
Question Number 186348 by test1234 last updated on 03/Feb/23 $$\mathrm{Q}{UIZ}: \\ $$$${If}\:{the}\:{sum}\:{of}\:{the}\:{numbers}\:\mathrm{1}\:{to}\:\mathrm{100}\:{can} \\ $$$${be}\:{calculated}\:{with}\:{Carl}\:{Gauss}'{s}\:{method}, \\ $$$${then}\:{How}\:{do}\:{we}\:{calculate}\:{the}\:{sum}\:{of}\:{the} \\ $$$${numbers}\:{starting}\:{from}\:\mathrm{2}\:{and}\:{going}\:{up}\:{to} \\ $$$$\mathrm{100}\:{by}\:{twos}\:{in}\:{an}\:{easy}\:{way}\:{with}\:{the}\:{same} \\ $$$${method}? \\ $$$${Or}\:\mathrm{2}+\mathrm{4}+\mathrm{6}+\mathrm{8}+\mathrm{10}+…+\mathrm{100}=? \\…
Question Number 120800 by mathocean1 last updated on 02/Nov/20 $${what}\:{remain}\:{when}\:{we}\:{divise} \\ $$$$\mathrm{2222}^{\mathrm{3333}\:} {by}\:\mathrm{3333}^{\mathrm{2222}} \\ $$ Commented by prakash jain last updated on 03/Nov/20 https://www.wolframalpha.com/input/?i=2222%5E3333+%28mod+3333%5E2222%29 Terms…
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Question Number 120654 by peter frank last updated on 01/Nov/20 $$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{dx}}{\left[\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\right]^{\mathrm{n}} } \\ $$ Answered by mindispower last updated on 01/Nov/20 $${x}={sh}\left({t}\right),{n}>\mathrm{1}…
Question Number 55059 by gunawan last updated on 17/Feb/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{root}\:\mathrm{equation} \\ $$$${z}^{\mathrm{4}} −\mathrm{5}{z}+\mathrm{1}=\mathrm{0}\:\mathrm{in}\:\mathrm{1}\:\leqslant\:\mid{z}\mid\:\leqslant\:\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com