Question Number 62180 by Mikael last updated on 17/Jun/19 $$\underset{{x}\rightarrow\infty} {{lim}}\:\frac{{senx}}{{x}} \\ $$ Commented by maxmathsup by imad last updated on 17/Jun/19 $${if}\:{you}\:{mean}\:{sinx}\:\:{we}\:{have}\:\:\mid{sinx}\mid\leqslant\mathrm{1}\:\Rightarrow\mid\frac{{sinx}}{{x}}\mid\leqslant\frac{\mathrm{1}}{\mid{x}\mid}\:\:{for}\:{all}\:{x}\neq\mathrm{0}\:\:{but} \\ $$$${lim}_{{x}\rightarrow\infty}…
Question Number 127501 by slahadjb last updated on 30/Dec/20 $${prove}\:{the}\:{convergence}\:{of}\:\left(\alpha_{{n}} \right)_{{n}\:} {such}\:{that}\: \\ $$$$\mathrm{tan}^{−\mathrm{1}} \left(\frac{\alpha_{{n}} }{{n}}\right)−\mathrm{2}\alpha_{{n}} +\mathrm{1}=\mathrm{0} \\ $$ Answered by mindispower last updated on…
Question Number 127459 by liberty last updated on 30/Dec/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{{x}}}}\:\right)^{{x}^{\mathrm{2}} } \:=?\: \\ $$ Answered by john_santu last updated on 30/Dec/20 $$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{x}}}}\:=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}+\frac{\mathrm{x}}{\mathrm{2x}+\mathrm{1}}}\:=\:\mathrm{1}+\frac{\mathrm{1}}{\frac{\mathrm{2x}^{\mathrm{2}} +\mathrm{2x}}{\mathrm{2x}+\mathrm{1}}} \\…
Question Number 192969 by mustafazaheen last updated on 01/Jun/23 Commented by mustafazaheen last updated on 01/Jun/23 $$\mathrm{how}\:\mathrm{is}\:\mathrm{solution}? \\ $$ Answered by MM42 last updated on…
Question Number 127421 by Study last updated on 29/Dec/20 $${li}\underset{{x}\rightarrow−\infty} {{m}}\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{3}}}{\mathrm{10}{x}−\mathrm{3}}=??? \\ $$ Answered by ebi last updated on 29/Dec/20 $$\underset{{x}\rightarrow−\infty} {{lim}}\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{3}}}{\mathrm{10}{x}−\mathrm{3}} \\…
Question Number 61834 by aliesam last updated on 09/Jun/19 Commented by maxmathsup by imad last updated on 09/Jun/19 $${let}\:{A}_{{n}} =\:\left\{\frac{\mathrm{1}}{{p}}\:\sum_{{k}=\mathrm{1}} ^{{p}} \:\left(\mathrm{1}+\frac{{k}}{{p}}\right)^{\frac{\mathrm{1}}{{n}}} \right\}^{{n}} \:\Rightarrow{ln}\left({A}_{{n}} \right)\:={n}\:{ln}\left(\frac{\mathrm{1}}{{p}}\sum_{{k}=\mathrm{1}}…
Question Number 192867 by beto last updated on 30/May/23 $${derivate}\:{of}\:\:{csc}\left(\mathrm{2}{x}\right)\:{by}\:\:{definition} \\ $$ Answered by cortano12 last updated on 02/Jun/23 $$\:\frac{\mathrm{d}\left(\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{2x}}\right)}{\mathrm{dx}}=\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{1}}{\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{2h}\right)}−\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{2x}}}{\mathrm{h}} \\ $$$$\:=\:\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}−\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{2h}\right)}{\mathrm{h}\:\mathrm{sin}\:\mathrm{2x}\:\mathrm{sin}\:\left(\mathrm{2x}+\mathrm{2h}\right)} \\…
Question Number 192846 by mathlove last updated on 29/May/23 $$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3}{h}}{\:\sqrt[{\mathrm{5}}]{\mathrm{3}{h}+{x}}−\sqrt[{\mathrm{5}}]{{x}}}=? \\ $$ Answered by MM42 last updated on 29/May/23 $${for}\:\:{f}\left({x}\right)=\sqrt[{\mathrm{5}}]{{x}}\:\Rightarrow{f}'\left({x}\right)=\frac{\mathrm{1}}{\mathrm{5}\sqrt[{\mathrm{5}}]{{x}^{\mathrm{4}} }} \\ $$$${lim}_{{h}\rightarrow\mathrm{0}} \frac{\mathrm{3}{h}}{\:\sqrt[{\mathrm{5}}]{\mathrm{3}{h}+{x}}−\sqrt[{\mathrm{5}}]{{x}}}=\frac{\mathrm{1}}{{f}'\left({x}\right)}=\mathrm{5}\sqrt[{\mathrm{5}}]{{x}^{\mathrm{4}}…
Question Number 192841 by TUN last updated on 29/May/23 Answered by witcher3 last updated on 02/Jun/23 $$\mathrm{f}\left(\mathrm{a}\right)=\int_{−\mathrm{a}} ^{\mathrm{a}} \frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\left(\mathrm{1}+\mathrm{e}^{\mathrm{bx}} \right)}\leqslant\int_{−\mathrm{a}} ^{\mathrm{a}} \frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)}=\mathrm{2tan}^{−\mathrm{1}} \left(\mathrm{a}\right)…
Question Number 127213 by Study last updated on 27/Dec/20 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left({cosx}\right)^{{logx}} =???\:\:\:\:{by}\:{sandiwich}\:{rule} \\ $$ Commented by Study last updated on 27/Dec/20 $${help}\:{me} \\ $$ Commented…