Question Number 76627 by Maclaurin Stickker last updated on 28/Dec/19 Commented by Maclaurin Stickker last updated on 28/Dec/19 $${If}\:{C}'\:{and}\:{B}'\:{are}\:{midpints}\:{of}\:{AC}\:{and} \\ $$$${AB},\:{find}\:{cot}\left(\theta\right)\:{as}\:{a}\:{function} \\ $$$${of}\:{angles}\:{B}\:{and}\:{C}. \\ $$…
Question Number 11089 by suci last updated on 11/Mar/17 $${for}\:{each}\:{n}\in\mathbb{N},\:{f}_{{n}} \left({x}\right)={nx}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{{n}} \\ $$$${for}\:{each}\:{x},\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:{a}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {f}_{{n}} \left({x}\right){dx} \\ $$$${if}\:{s}_{{n}} ={sin}\left(\pi{a}_{{n}} \right),\:{for}\:{each}\:{n}\in\mathbb{N},\:{then} \\ $$$${l}\underset{{n}\rightarrow\sim} {{i}m}\:{s}_{{n}}…
Question Number 11088 by suci last updated on 11/Mar/17 $${S}=\left\{\frac{{n}}{\mathrm{2}{m}}\:+\:\frac{\mathrm{6}{m}}{{n}}\::\:{n},{m}\in\mathbb{N}\right\} \\ $$$${inf}\left({S}\right)=…???\:{and}\:{sup}\left({S}\right)=…??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 76622 by Sathvik last updated on 28/Dec/19 $$\mathrm{Find}\:\left(\mathrm{a}.\mathrm{b}.\mathrm{c}\right)\:\mathrm{for}\:\mathrm{equation}\:\mathrm{acos}\:\mathrm{2x}+\mathrm{bsin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{c}=\mathrm{0}\:\mathrm{is}\:\mathrm{satisfied}\:\mathrm{by}\:\mathrm{every}\:\mathrm{x} \\ $$ Answered by MJS last updated on 28/Dec/19 $${a}\mathrm{cos}\:\mathrm{2}{x}\:+{b}\mathrm{sin}^{\mathrm{2}} \:{x}\:+{c}=\mathrm{0} \\ $$$${a}\mathrm{cos}\:\mathrm{2}{x}\:+{b}×\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right)+{c}=\mathrm{0} \\…
Question Number 11087 by suci last updated on 11/Mar/17 $${a}<\frac{\pi}{\mathrm{2}} \\ $$$${if}\:{M}<\mathrm{1}\:{with}\:\mid{cos}\:{x}−{cos}\:{y}\mid\leqslant{M}\mid{x}−{y}\mid \\ $$$${to}\:{each}\:{x},{y}\in\left[\mathrm{0},{a}\right] \\ $$$${M}=….??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 142149 by cesarL last updated on 27/May/21 $$\mathrm{6}.\:\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$$$\mathrm{7}.\:\int\frac{\mathrm{4}{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}} \\ $$$$\mathrm{8}.\:\int\frac{\mathrm{3}−\mathrm{2}{xdx}}{{x}^{\mathrm{2}} −\mathrm{64}} \\ $$$$\mathrm{9}.\:\int\frac{\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}{x}}{dx} \\ $$$$\mathrm{10}.\:\int\frac{\mathrm{4}−\mathrm{3}{x}}{{x}^{\mathrm{3}} −\mathrm{2}{x}}{dx} \\…
Question Number 142148 by islamo last updated on 27/May/21 $$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}!}=? \\ $$ Answered by mathmax by abdo last updated on 27/May/21 $$\mathrm{e}^{\mathrm{x}} =\sum_{\mathrm{n}=\mathrm{0}}…
Question Number 76615 by mhmd last updated on 28/Dec/19 $$\int{sec}^{\mathrm{3}} {x}\:{dx} \\ $$ Answered by $@ty@m123 last updated on 28/Dec/19 $$\int\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} {x}}.\mathrm{sec}\:^{\mathrm{2}} {xdx} \\ $$$$\int\sqrt{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 11078 by 3494 last updated on 10/Mar/17 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Answered by FilupS last updated on 11/Mar/17…
Question Number 142151 by iloveisrael last updated on 27/May/21 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\sqrt{{x}+\mathrm{1}}−\mathrm{sin}\:\sqrt{{x}}\:=? \\ $$ Commented by gsk2684 last updated on 27/May/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}\:\mathrm{cos}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{x}}}{\mathrm{2}}\mathrm{sin}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}}}{\mathrm{2}}\right) \\ $$$$\mathrm{2}\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{cos}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}−\sqrt{\mathrm{x}}}{\mathrm{2}}\mathrm{sin}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{x}}}\right)…