Question Number 133277 by Engr_Jidda last updated on 20/Feb/21 $${use}\:{weierstrass}\:{m}−{test}\:{and}\:{dirichlet} \\ $$$${test}\:{to}\:{confirm}\:{the}\:{uniformly}\:{covergence} \\ $$$${of}\:{the}\:{following}\:{series}\:{in}\:{the}\:{interval}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\left.{a}\right)\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cosnx}}{{n}^{\mathrm{4}} } \\ $$$$\left.{b}\right)\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cosnx}}{{n}^{\frac{\mathrm{8}}{\mathrm{7}}} } \\…
Question Number 133161 by abdullahquwatan last updated on 19/Feb/21 $$\mathrm{give}\:\mathrm{me}\:\mathrm{problems}\:\mathrm{algebra}\:\mathrm{limit}\:\mathrm{function}\:\mathrm{hard} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133114 by bemath last updated on 19/Feb/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}\:\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\right)^{\mathrm{x}^{\mathrm{2}} +\mathrm{sin}\:\mathrm{3x}} ? \\ $$ Answered by bobhans last updated on 19/Feb/21 $${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\sqrt{{x}^{\mathrm{2}}…
Question Number 133091 by metamorfose last updated on 18/Feb/21 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{t}^{\mathrm{2}} \right)^{\mathrm{3}} {cos}\left({xt}\right){dt}…? \\ $$ Answered by mnjuly1970 last updated on 18/Feb/21 $${answer}:=\mathrm{0}…
Question Number 133068 by mnjuly1970 last updated on 18/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{advanced}…..{calculus}…. \\ $$$$\:\:\:{evaluation}::\:\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}} \left(\:\frac{\zeta\left({k}\right)−\mathrm{1}}{{k}}\right) \\ $$$$\:\:\:\::::\boldsymbol{\Phi}=\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}} \:\frac{\zeta\left({k}\right)−\mathrm{1}}{{k}} \\ $$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\underset{{n}=\mathrm{2}}…
Question Number 132971 by metamorfose last updated on 17/Feb/21 $$\:\:{Lim}_{{x}\rightarrow\left(\frac{\pi}{\mathrm{2}}\right)^{−\:\:\:} } \frac{\lfloor{sin}\left({x}\right)\rfloor}{{cos}\left({x}\lfloor{x}\rfloor\right)} \\ $$ Answered by mnjuly1970 last updated on 18/Feb/21 $${ans}:\frac{\mathrm{0}}{\mathrm{0}^{+} }=\mathrm{0} \\ $$…
Question Number 132928 by metamorfose last updated on 17/Feb/21 $$\underset{{k}=\mathrm{1}} {\overset{+\infty} {\sum}}\left(−\mathrm{1}\right)^{{k}} {ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{k}}\right) \\ $$ Commented by Olaf last updated on 17/Feb/21 $${sorry}\:{sir},\:{I}\:{deleted}\:{my}\:{answer}. \\ $$$${it}\:{was}\:{wrong}.…
Question Number 1817 by 112358 last updated on 05/Oct/15 $${Evaluate}\:{the}\:{following}\:{limit}, \\ $$$${if}\:{it}\:{exists}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sin}\left({sin}\left({sinx}\right)\right)}{{x}}. \\ $$ Answered by 123456 last updated on 05/Oct/15 $${f}_{{n}}…
Question Number 1766 by Rasheed Ahmad last updated on 18/Sep/15 $${Determine}\: \\ $$$$\:\:\left({i}\right)\:\:\underset{{a}\rightarrow\infty} {{lim}}\:{a}^{\frac{\mathrm{1}}{{a}}} \:\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:\underset{{a}\rightarrow\mathrm{0}} {{lim}}\:{a}^{\frac{\mathrm{1}}{{a}}} \\ $$ Answered by 123456 last updated on 19/Sep/15…
Question Number 1767 by Rasheed Ahmad last updated on 18/Sep/15 $${Determine} \\ $$$$\:\left({i}\right)\:\underset{{a}\rightarrow\infty} {{lim}}\:\left(\frac{\mathrm{1}}{{a}}\right)^{{a}} \:\:\:\left({ii}\right)\:\:\underset{{a}\rightarrow\mathrm{0}} {{lim}}\:\left(\frac{\mathrm{1}}{{a}}\right)^{{a}} \: \\ $$ Answered by 123456 last updated on…