Question Number 66341 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{k}^{\mathrm{3}} }{\:\sqrt{\left(\mathrm{1}+\left(\frac{{k}}{{n}}\right)^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$ Commented by Prithwish sen…
Question Number 66324 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\mathrm{2}^{{n}} \:+{ln}\left({n}\right)} \\ $$ Commented by mathmax by abdo last updated…
Question Number 66322 by mathmax by abdo last updated on 12/Aug/19 $${let}\:{f}\left({x}\right)=\left({cosx}\right)^{\frac{\mathrm{1}}{{x}}} \:\left(\:\mathrm{1}\right)\:\:{prove}\:{that}\:{f}\left({x}\right)\sim\mathrm{1}−\frac{{x}}{\mathrm{2}}+\frac{{x}^{\mathrm{2}} }{\mathrm{8}}\:\:\left(\:{x}\rightarrow\mathrm{0}\right) \\ $$$$\left(\mathrm{2}\right){ptove}\:{that}\:{f}^{'} \left({x}\right)\sim−\frac{\mathrm{2}}{\pi}\:{e}^{\left(\frac{\mathrm{1}}{{x}}−\mathrm{1}\right){ln}\left({cosx}\right)} \:\:\left({x}\rightarrow\frac{\pi}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 66323 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\:\:\frac{{x}\left(\mathrm{1}+{cosx}\right)−\mathrm{2}{tanx}}{\mathrm{2}{x}−{sinx}−{tanx}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66318 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)^{\frac{\mathrm{1}}{{sinx}}} \\ $$ Commented by mathmax by abdo last updated on 24/Aug/19 $${let}\:{f}\left({x}\right)=\left(\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}\right)^{\frac{\mathrm{1}}{{sinx}}}…
Question Number 66321 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\:\left({tan}\left(\frac{\pi}{\mathrm{2}+{x}}\right)\right)^{{x}} \\ $$ Commented by mathmax by abdo last updated on 24/Aug/19…
Question Number 66316 by mathmax by abdo last updated on 12/Aug/19 $${lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{ln}\left({sin}^{\mathrm{2}} {x}\right)}{\left(\frac{\pi}{\mathrm{2}}−{x}\right)^{\mathrm{2}} } \\ $$$$ \\ $$ Commented by mathmax by abdo last…
Question Number 66319 by mathmax by abdo last updated on 12/Aug/19 $${find}\:{lim}_{{x}\rightarrow+\infty} \:\:\:\:\left(\frac{{a}^{\frac{\mathrm{1}}{{x}}} \:+\mathrm{2}{b}^{\frac{\mathrm{1}}{{x}}} +\mathrm{3}{c}^{\frac{\mathrm{1}}{{x}}} }{\mathrm{6}}\right)^{{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 66317 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{ln}\left({cosx}\right)}{\mathrm{1}−{cos}\left(\mathrm{2}{x}\right)} \\ $$ Commented by kaivan.ahmadi last updated on 12/Aug/19 $$\equiv{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left({cosx}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\overset{{hop}}…
Question Number 66304 by mathmax by abdo last updated on 12/Aug/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{ln}\left({x}+\mathrm{1}+{sin}\left(\pi{x}\right)\right)}{{xsin}\left(\mathrm{2}{x}\right)} \\ $$ Answered by kaivan.ahmadi last updated on 12/Aug/19 $$\equiv{lim}_{{x}\rightarrow\mathrm{0}} \frac{{ln}\left({x}+\mathrm{1}+\pi{x}\right)}{\mathrm{2}{x}^{\mathrm{2}} }\:\overset{{hop}}…