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…
Question Number 1608 by 112358 last updated on 26/Aug/15 $${Find}\:{the}\:{limit}\:{of}\:{this}\:{sequence}. \\ $$$$\sqrt{\mathrm{2}},\sqrt{\mathrm{2}\sqrt{\mathrm{2}}},\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}},\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}}},… \\ $$$${Show}\:{that}\:{the}\:{sum}\:{of}\:{the} \\ $$$${terms}\:{of}\:{this}\:{infinite}\:{sequence} \\ $$$${does}\:{not}\:{converge}. \\ $$ Commented by Rasheed Ahmad last…
Question Number 1499 by 112358 last updated on 14/Aug/15 $${Use}\:{the}\:\epsilon−\delta\:{definition}\:{of}\:{the} \\ $$$${limit}\:{to}\:{show}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{{x}}{\mathrm{6}−{x}}=\mathrm{1}\:. \\ $$$$\left({I}'{m}\:{hoping}\:{to}\:{better}\:{understand}\right. \\ $$$${this}\:{concept}\:{by}\:{example}\:{so}\:{please} \\ $$$${help}\:{me}\:{by}\:{explaning}\:{the}\: \\ $$$$\left.{reasoning}\:{behind}\:{your}\:{steps}.\right) \\ $$…
Question Number 132550 by liberty last updated on 15/Feb/21 $$\mathrm{If}\:{a}=\mathrm{1}\:\mathrm{then}\:\underset{{x}\rightarrow\left({a}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{5}\right)} {\mathrm{lim}}\frac{−\mathrm{4}{x}^{\mathrm{2}} +\sqrt{\mathrm{3}{x}+\mathrm{1}}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{8}{x}}+\mathrm{2}}\:=? \\ $$$$\left(\mathrm{a}\right)\:−\mathrm{1}\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:−\frac{\mathrm{4}}{\mathrm{5}}\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:−\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\left(\mathrm{d}\right)\:−\frac{\mathrm{2}}{\mathrm{5}}\:\:\:\:\left(\mathrm{e}\right)\:−\frac{\mathrm{1}}{\mathrm{5}} \\ $$ Commented by MJS_new last updated…
Question Number 132483 by abdullahquwatan last updated on 14/Feb/21 $$\underset{{x}\rightarrow−\mathrm{2}} {\mathrm{lim}}\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}−{x}^{\mathrm{2}} +\mathrm{2}}{{x}^{\mathrm{5}} +\mathrm{32}}\:\mathrm{no}\:\mathrm{hospital} \\ $$ Commented by EDWIN88 last updated on 14/Feb/21 $$\mathrm{what}\:\mathrm{hospital}? \\…
Question Number 66927 by Cmr 237 last updated on 21/Aug/19 $${calcul}\:{la}\:{limite}\:{suivante}: \\ $$$${lim}\:\:\:\:\:\:\:\left(\frac{\mathrm{1}^{{x}} +\mathrm{2}^{{x}} +\mathrm{3}^{{x}} +……+{n}^{{x}} }{{n}}\right)^{\frac{\mathrm{1}}{{x}}} =\mathrm{A} \\ $$$${x}\rightarrow\mathrm{0} \\ $$$$\mathrm{trouve}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\boldsymbol{\mathrm{A}} \\ $$$$\mathrm{trouve}\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{de}\:\boldsymbol{\mathrm{P}}\:\mathrm{definir}\:\mathrm{par}: \\…
Question Number 1368 by prakash jain last updated on 25/Jul/15 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{ln}\left({ax}+{b}\right)}{\mathrm{ln}\:\left({bx}+{a}\right)}\:=? \\ $$ Commented by 123456 last updated on 25/Jul/15 $${f}\left({x}\right)=\frac{\mathrm{ln}\:\left({ax}+{b}\right)}{\mathrm{ln}\:\left({bx}+{a}\right)} \\ $$$$\frac{\frac{{d}}{{dx}}\left[\mathrm{ln}\:\left({ax}+{b}\right)\right]}{\frac{{d}}{{dx}}\left[\mathrm{ln}\:\left({bx}+{a}\right)\right]}=\frac{\frac{{a}}{{ax}+{b}}}{\frac{{b}}{{bx}+{a}}}=\frac{{a}\left({bx}+{a}\right)}{{b}\left({ax}+{b}\right)}\rightarrow\frac{{ab}}{{ba}}=\mathrm{1} \\…
Question Number 66862 by Aman Arya last updated on 20/Aug/19 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}3}{x}^{\mathrm{5}} \\ $$ Commented by mathmax by abdo last updated on 20/Aug/19 $$=\mathrm{3}×\mathrm{0}=\mathrm{0} \\…
Question Number 132367 by Raxreedoroid last updated on 13/Feb/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{x}^{{n}} }{\Gamma\left({n}+\mathrm{1}\right)} \\ $$ Answered by TheSupreme last updated on 13/Feb/21 $${if}\:{n}\in\mathbb{N}\:\rightarrow\:\Gamma\left({n}+\mathrm{1}\right)={n}! \\ $$$$\mathrm{lim}\:\frac{\mathrm{x}^{\mathrm{n}} }{\mathrm{n}!}=\mathrm{0}\:\forall{x}\in\mathbb{R}_{\mathrm{0}}…
Question Number 132356 by Raxreedoroid last updated on 13/Feb/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{x}^{{n}} }{{n}!}+\frac{\mathrm{1}}{\mathrm{2}\left(\mathrm{ln}\:\mathrm{2}\right)^{{n}} }\right)=?\:,{x}\in\mathbb{R} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com