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Category: Limits

lim-x-x-2-1-x-x-1-x-x-3-1-x-x-1-x-

Question Number 185405 by greougoury555 last updated on 21/Jan/23 $$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left({x}+\mathrm{2}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }{\left({x}+\mathrm{3}\right)^{\mathrm{1}/{x}} −{x}^{\mathrm{1}/{x}} }\:=? \\ $$ Answered by Frix last updated on 22/Jan/23 $$=\underset{{t}\rightarrow\mathrm{0}^{+}…

If-a-b-c-and-d-are-constants-such-that-lim-x-0-ax-2-sin-bx-sin-cx-sin-dx-3x-2-5x-4-7x-6-8-find-the-value-of-the-sum-a-b-c-d-

Question Number 185406 by greougoury555 last updated on 21/Jan/23 $${If}\:{a},{b},{c}\:{and}\:{d}\:{are}\:{constants}\:{such}\:{that} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{ax}^{\mathrm{2}} +\mathrm{sin}\:{bx}+\mathrm{sin}\:{cx}+\mathrm{sin}\:{dx}}{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{7}{x}^{\mathrm{6}} }=\mathrm{8} \\ $$$${find}\:{the}\:{value}\:{of}\:{the}\:{sum}\:{a}+{b}+{c}+{d} \\ $$ Answered by witcher3 last…

lim-x-1-1-2n-n-e-1-2-n-n-e-2-

Question Number 119867 by Study last updated on 27/Oct/20 $${li}\underset{{x}\rightarrow\infty} {{m}}\frac{\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}{n}}\right)^{{n}} −\sqrt{{e}}}{\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)^{{n}} −{e}^{\mathrm{2}} }=??? \\ $$ Commented by Dwaipayan Shikari last updated on 27/Oct/20 $$\frac{\mathrm{1}}{\mathrm{16}}{e}^{−\frac{\mathrm{3}}{\mathrm{2}}}…

lim-x-pi-4-4-2-cos-x-sin-x-5-cos-x-sin-x-2-

Question Number 119725 by bemath last updated on 26/Oct/20 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{4}\sqrt{\mathrm{2}}−\left(\mathrm{cos}\:{x}+\mathrm{sin}\:{x}\right)^{\mathrm{5}} }{\left(\mathrm{cos}\:{x}−\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:=? \\ $$ Commented by bemath last updated on 26/Oct/20 $${compare}\:{via}\:{L}'{Hopital} \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}}…

Question-185209

Question Number 185209 by Rupesh123 last updated on 18/Jan/23 Answered by som(math1967) last updated on 18/Jan/23 $$\left.{a}\right)\:\underset{{n}\rightarrow\infty} {{lim}}\:\frac{\mathrm{1}}{{n}}\left[\:\left(\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2022}} +\left(\frac{\mathrm{2}}{{n}}\right)^{\mathrm{2022}} +…\left(\frac{{n}}{{n}}\right)^{\mathrm{2022}} \right] \\ $$$$\underset{{n}\rightarrow\infty} {{lim}}\:\frac{\mathrm{1}}{{n}}\underset{{r}=\mathrm{1}} {\overset{{n}}…

Question-119629

Question Number 119629 by 9764954060 last updated on 25/Oct/20 Answered by TANMAY PANACEA last updated on 25/Oct/20 $${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\ $$$${so}\:{here}\:{x}=\frac{−\mathrm{3}\pm\sqrt{\mathrm{3}^{\mathrm{2}} −\mathrm{4}×\mathrm{2}×\mathrm{7}}}{\mathrm{2}×\mathrm{2}}=\frac{−\mathrm{3}\pm\sqrt{−\mathrm{47}}}{\mathrm{4}}…

lim-x-sin-x-1-x-sin-x-

Question Number 119517 by bemath last updated on 25/Oct/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left[\:\mathrm{sin}\:\left({x}+\frac{\mathrm{1}}{{x}}\right)−\mathrm{sin}\:{x}\:\right]\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 25/Oct/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({sin}\left({x}+\frac{\mathrm{1}}{{x}}\right)−{sinx}\right) \\ $$$$=\underset{{x}\rightarrow\infty}…