Question Number 201000 by mokys last updated on 27/Nov/23 $${find}\: \\ $$$$ \\ $$$$\left.\:\mathrm{1}\right)\left(\mathrm{0},\mathrm{2}\right)\:\cup\:\left\{\mathrm{3}\right\}\:\: \\ $$$$ \\ $$$$\left.\:\:\mathrm{2}\right)\left[\mathrm{0},\mathrm{2}\right]\:\cup\:\left\{\mathrm{3}\right\} \\ $$$$ \\ $$$$\left.\:\:\mathrm{3}\right)\:\left(−\mathrm{5},\mathrm{5}\right)\:\cup\:\left\{\mathrm{6}\right\} \\ $$$$\:\: \\…
Question Number 200960 by sonukgindia last updated on 27/Nov/23 Answered by Frix last updated on 27/Nov/23 $${t}=\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$\Rightarrow \\ $$$$\int…=\int\left(\mathrm{1}−\frac{\mathrm{1}}{{t}}\right){dt}={t}−\mathrm{ln}\:{t}\:= \\ $$$$=\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{ln}\:\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}}…
Question Number 200894 by sonukgindia last updated on 26/Nov/23 Answered by Frix last updated on 26/Nov/23 $$=\mathrm{4}\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\frac{{dx}}{\mathrm{1}+\mathrm{4sin}^{\mathrm{2}} \:{x}}\:\overset{{t}=\mathrm{tan}\:{x}} {=} \\ $$$$=\mathrm{4}\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{dt}}{\mathrm{5}{t}^{\mathrm{2}}…
Question Number 200895 by sonukgindia last updated on 26/Nov/23 Answered by mathematicsmagic last updated on 26/Nov/23 $${beta}\:{functions}\:,{we}\:{put}\:{x}^{\varphi} ={t} \\ $$ Terms of Service Privacy Policy…
Question Number 200934 by sonukgindia last updated on 26/Nov/23 Answered by Frix last updated on 27/Nov/23 $$\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\mathrm{2}}} {\int}}\left(\mathrm{tan}\:\pi{x}\right)^{\frac{\mathrm{4}}{\mathrm{5}}} {dx}\:\overset{{t}=\left(\mathrm{cot}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{5}}} } {=} \\ $$$$=−\frac{\mathrm{5}}{\pi}\underset{\infty} {\overset{\mathrm{0}}…
Question Number 200925 by akolade last updated on 26/Nov/23 Answered by mr W last updated on 26/Nov/23 $$\boldsymbol{{p}}=\overset{\rightarrow} {{AB}}=\left(\mathrm{6},\:−\mathrm{14}\right) \\ $$$${C}=\left(\mathrm{1},\mathrm{5}\right)+\frac{\mathrm{1}}{\mathrm{4}}\left(\mathrm{6},\:−\mathrm{14}\right)=\left(\mathrm{2}.\mathrm{5},\:\mathrm{1}.\mathrm{5}\right) \\ $$$${D}=\left(\mathrm{1},\mathrm{5}\right)+\frac{\mathrm{2}}{\mathrm{4}}\left(\mathrm{6},\:−\mathrm{14}\right)=\left(\mathrm{4},\:−\mathrm{2}\right) \\ $$$${E}=\left(\mathrm{1},\mathrm{5}\right)+\frac{\mathrm{3}}{\mathrm{4}}\left(\mathrm{6},\:−\mathrm{14}\right)=\left(\mathrm{5}.\mathrm{5},\:−\mathrm{5}.\mathrm{5}\right)…
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Question Number 200903 by MrGHK last updated on 26/Nov/23 Answered by witcher3 last updated on 26/Nov/23 $$\mathrm{Hint} \\ $$$$\left(−\mathrm{1}\right)^{\mathrm{n}} \left(\Psi\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right)−\mathrm{ln}\left(\mathrm{n}\right)\right)=\underset{\mathrm{n}\geqslant\mathrm{1}} {\sum}\left(\mathrm{ln}\left(\frac{\mathrm{2n}+\mathrm{1}}{\mathrm{2n}}\right)+\Psi\left(\mathrm{2n}+\frac{\mathrm{1}}{\mathrm{2}}\right)−\Psi\left(\mathrm{2n}+\frac{\mathrm{3}}{\mathrm{2}}\right)\right) \\ $$$$=\underset{{x}\rightarrow\infty} {\mathrm{lim}ln}\left(\underset{\mathrm{1}} {\overset{\mathrm{x}}…
Question Number 200860 by liuxinnan last updated on 25/Nov/23 $${when}\:{x}\in\left[\mathrm{0},\infty\right) \\ $$$$\left({x}+{m}\right){e}^{\mathrm{2}{x}} −{x}^{\mathrm{2}} \geqslant\left({x}+{m}\right){ln}\left({x}+{m}\right) \\ $$$${m}\in? \\ $$ Answered by witcher3 last updated on 25/Nov/23…
Question Number 200861 by sonukgindia last updated on 25/Nov/23 Answered by Mathspace last updated on 25/Nov/23 $${J}=_{{x}={t}^{\frac{\mathrm{1}}{\mathrm{10}}} } \frac{\mathrm{1}}{\mathrm{10}}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{5}}{\mathrm{1}+{t}}{t}^{\frac{\mathrm{1}}{\mathrm{10}}−\mathrm{1}} {dt} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{\mathrm{0}} ^{\infty}…