Question Number 105106 by bemath last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\pi\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{\mathrm{3}{x}^{\mathrm{2}} }\:? \\ $$ Answered by bramlex last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\pi\:\mathrm{cos}\:^{\mathrm{2}} {x}\right)}{\mathrm{3}{x}^{\mathrm{2}}…
Question Number 105036 by bobhans last updated on 25/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}.\left[\:\frac{\mathrm{1}}{{x}}\:\right]\:? \\ $$$${note}\:\left[\:\right]\:=\:{greatest}\:{integer}\:{function} \\ $$ Answered by john santu last updated on 25/Jul/20 $${the}\:{limit}\:{as}\:{x}\rightarrow\mathrm{0}^{+} \:{can}\:{be}…
Question Number 170565 by cortano1 last updated on 27/May/22 Answered by Mathspace last updated on 27/May/22 $${f}^{'} \left({x}\right)={x}^{\mathrm{3}} \frac{\mathrm{2}\left({x}+\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{1}−\mathrm{3}\left({x}+\mathrm{2}\right)^{\mathrm{4}} }−{x}^{\mathrm{3}} \frac{\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{1}−\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{4}} } \\…
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Question Number 170551 by 2407 last updated on 26/May/22 Answered by JDamian last updated on 26/May/22 $$\mathrm{3} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 170547 by qaz last updated on 26/May/22 $$\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}}\sqrt[{\mathrm{3}}]{\mathrm{x}}\int_{\mathrm{x}} ^{\mathrm{x}+\mathrm{1}} \frac{\mathrm{sin}\:\mathrm{t}}{\:\sqrt{\mathrm{t}+\mathrm{cos}\:\mathrm{t}}}\mathrm{dt}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 170537 by 2407 last updated on 26/May/22 Commented by cortano1 last updated on 26/May/22 $$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{{n}}\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{n}}}}\:−\sqrt{{n}}\:= \\ $$$$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{{n}}\:\left(\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{n}}}}\:−\mathrm{1}\right)= \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$…
Question Number 104899 by bramlex last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cos}\:\left(\mathrm{sin}\:{x}\right)−\mathrm{cos}\:\left({x}\right)}{{x}^{\mathrm{4}} }\:?\: \\ $$ Answered by john santu last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−\mathrm{2sin}\:\left(\frac{{x}+\mathrm{sin}\:{x}}{\mathrm{2}}\right)\mathrm{sin}\:\left(\frac{\mathrm{sin}\:{x}−{x}}{\mathrm{2}}\right)}{{x}^{\mathrm{4}} }…
Question Number 104850 by ~blr237~ last updated on 24/Jul/20 $${Let}\:\:{E}\:{be}\:{a}\:{no}\:{empty}\:{set}\:{with}\:{card}={n}\geqslant\mathrm{1} \\ $$$$\:{Find}\:{in}\:{term}\:{of}\:\:{n}\:\:\:\:\:\:\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}−{B}\right)=\underset{{A},{B}\subseteq{E}} {\sum}{Card}\left({A}\cap{B}\right)=\frac{\mathrm{1}}{\mathrm{3}}\underset{{A},{B}\subseteq{E}} {\sum}{Card}\:\left({A}\cup{B}\right)={n}\mathrm{4}^{{n}−\mathrm{1}} \:\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 104838 by bramlex last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\:^{\mathrm{3}} \left(\mathrm{8}{x}\right)−\mathrm{1}}{\mathrm{6}{x}^{\mathrm{2}} }\:? \\ $$ Answered by john santu last updated on 24/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{8}{x}−\mathrm{1}\right)\left(\mathrm{cos}\:^{\mathrm{2}}…