Question Number 195148 by horsebrand11 last updated on 25/Jul/23 $$\:\:\begin{array}{|c|}{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{x}\:\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}=?}\\\hline\end{array} \\ $$ Answered by Erico last updated on 25/Jul/23 $$\frac{\mathrm{1}+\mathrm{xsinx}−\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}=\frac{\mathrm{1}−\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}+\frac{\mathrm{x}}{\mathrm{sinx}} \\…
Question Number 195136 by mathlove last updated on 25/Jul/23 $${f}\left({x}\right)={arctan}\left({sinx}\right) \\ $$$${and}\:\:{cosa}=\frac{\mathrm{2}}{\mathrm{3}}\:\:\:\:\:\:\:\:{faind}\:\:\:{f}^{'} \left({a}\right)=? \\ $$ Answered by som(math1967) last updated on 25/Jul/23 $$\:\boldsymbol{{f}}\:'\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}}×\boldsymbol{{cosx}} \\…
Question Number 195093 by Braulio last updated on 24/Jul/23 Answered by cortano12 last updated on 24/Jul/23 Answered by MM42 last updated on 24/Jul/23 $${hop}\rightarrow{lim}_{{x}\rightarrow\pi} \:\frac{\frac{\mathrm{1}}{\mathrm{2}}{cos}\frac{{x}}{\mathrm{2}}−{sinx}}{\mathrm{2}{sinxcosx}−{sinx}}…
Question Number 195092 by mathlove last updated on 24/Jul/23 $$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\mathrm{4}{x}+\mathrm{5}}{{x}−{x}^{\mathrm{2}} }=? \\ $$ Answered by tri26112004 last updated on 24/Jul/23 $${We}\:{have}: \\ $$$$\bullet\underset{{x}\rightarrow\mathrm{1}^{+}…
Question Number 195065 by alcohol last updated on 23/Jul/23 Answered by Rasheed.Sindhi last updated on 23/Jul/23 $${Let}\:{a}−{d},{a},{a}+{d}\:{are}\:{required}\:{numbers} \\ $$$$\left({a}−{d}\right)+{a}+\left({a}+{d}\right)=\mathrm{21} \\ $$$$\mathrm{3}{a}=\mathrm{21}\Rightarrow{a}=\mathrm{7} \\ $$$$\therefore\:\:\mathrm{7}−{d},\mathrm{7},\mathrm{7}+{d}\:{are}\:{required}\:{numbers} \\ $$$${Now}\:{by}\:{given}:\:…
Question Number 195066 by alcohol last updated on 23/Jul/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 195075 by tri26112004 last updated on 23/Jul/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}}{{x}} \\ $$ Answered by MM42 last updated on 23/Jul/23 $$\exists\:{m}>\mathrm{0}\:;\:\forall\:{x}\in\mathbb{R}\:\Rightarrow\:\mid{sin}^{\mathrm{2}} {x}−{cos}^{\mathrm{3}} {x}\mid\leqslant{m}…
Question Number 195033 by mathlove last updated on 22/Jul/23 $${any}\:{point}\:{is}\:{the}\:{function}\:{is} \\ $$$${not}\:{continous} \\ $$$${f}\left({x}\right)=\left(\mathrm{4}{x}+\mathrm{8}\right)^{\frac{{ln}\mathrm{45}}{\mathrm{8}}} \\ $$$$\left.{a}\left.\right)\:−\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}\right)\:−\mathrm{2} \\ $$$$\left.{c}\left.\right)\:{no}\:{one}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}\right)\:\mathrm{5} \\ $$ Answered by alephzero last updated…
Question Number 195029 by cortano12 last updated on 22/Jul/23 $$\:\:\:\:\underbrace{ } \\ $$ Answered by MM42 last updated on 22/Jul/23 $${lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\frac{\sqrt{\mathrm{1}+{x}}−\mathrm{1}}{\:\sqrt{\mathrm{3}}{ln}\left(\mathrm{1}+{x}\right)}\:=\overset{{hop}} {\rightarrow}\: \\…
Question Number 195021 by tri26112004 last updated on 22/Jul/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−{sin}\:{x}}{{x}^{{n}} }=¿\:\left({n}\in{N}^{\ast} \right) \\ $$ Answered by MM42 last updated on 22/Jul/23 $${if}\:\:{x}\rightarrow\mathrm{0}\:\Rightarrow\:{x}−{sinx}\:\sim\:\frac{\mathrm{1}}{\mathrm{6}}{x}^{\mathrm{3}} \\ $$$$\Rightarrow{if}\:\:\:{n}<\mathrm{3}\:\Rightarrow\:{lim}=\mathrm{0}…