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Category: Limits

lim-x-0-2tan-x-5sin-x-3x-x-3-1-1-2x-3-1-5-

Question Number 124915 by liberty last updated on 06/Dec/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2tan}\:{x}−\mathrm{5sin}\:{x}+\mathrm{3}{x}−{x}^{\mathrm{3}} }{\mathrm{1}−\sqrt[{\mathrm{5}}]{\mathrm{1}−\mathrm{2}{x}^{\mathrm{3}} }}\:=?\: \\ $$ Answered by bemath last updated on 07/Dec/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}\left({x}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}}\right)−\mathrm{5}\left({x}−\frac{{x}^{\mathrm{3}}…

lim-x-x-1-1-4-x-1-4-x-1-1-3-x-1-3-

Question Number 124802 by john_santu last updated on 06/Dec/20 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{4}}]{{x}+\mathrm{1}}\:−\:\sqrt[{\mathrm{4}}]{{x}}}{\:\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}\:−\:\sqrt[{\mathrm{3}}]{{x}}}\:=?\: \\ $$ Answered by bramlexs22 last updated on 06/Dec/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{4}}]{{x}}\:\left(\sqrt[{\mathrm{4}}]{\mathrm{1}+\frac{\mathrm{1}}{{x}}}−\mathrm{1}\right)}{\:\sqrt[{\mathrm{3}}]{{x}}\:\left(\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{1}}{{x}}}−\mathrm{1}\right)}\:= \\ $$$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{12}}]{{x}}}\:\left(\frac{\sqrt[{\mathrm{4}\:}]{\mathrm{1}+\frac{\mathrm{1}}{{x}}}\:−\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{\mathrm{1}+\frac{\mathrm{1}}{{x}}}−\mathrm{1}}\right)\:=\:\mathrm{0}…

lim-x-0-sin-x-tan-x-x-3-a-1-2-b-1-4-c-1-2-d-1-4-

Question Number 190300 by mnjuly1970 last updated on 31/Mar/23 $$ \\ $$$$\:\:\:\mathrm{lim}_{\:{x}\rightarrow\mathrm{0}} \frac{\:{sin}\left({x}\right)\:−{tan}\left({x}\right)}{{x}^{\:\mathrm{3}} } \\ $$$$\:\:\:\:\:{a}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:{b}:\:\:\:\:\frac{−\mathrm{1}}{\mathrm{4}}\:\:\:\:\:\:\:\:\:{c}:\:\:\:\:\:\frac{−\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:{d}:\:\:\:\:\frac{−\mathrm{1}}{\mathrm{4}} \\ $$$$ \\ $$ Answered by som(math1967) last updated…

Lim-x-pi-2-sinx-sinx-sinx-1-sinx-logsinx-a-4-b-2-c-1-2-d-none-

Question Number 190182 by SLVR last updated on 29/Mar/23 $${Li}\underset{{x}\rightarrow\pi/\mathrm{2}} {{m}}\frac{{sinx}−{sinx}^{{sinx}} }{\mathrm{1}−{sinx}+{logsinx}} \\ $$$$\left.{a}\left.\right)\left.\mathrm{4}\left.\:\:\:\:\:\:\:\:{b}\right)\mathrm{2}\:\:\:\:\:\:\:\:\:\:{c}\right)\mathrm{1}/\mathrm{2}\:\:\:\:\:\:\:\:{d}\right){none} \\ $$ Commented by SLVR last updated on 29/Mar/23 $${kindly}\:{help}\:{me} \\…

calculate-lim-n-n-3-2-n-3-2-n-2-

Question Number 190178 by mnjuly1970 last updated on 29/Mar/23 $$ \\ $$$$\:\:{calculate} \\ $$$$ \\ $$$$\:\:\:\:\mathrm{lim}_{\:\mathrm{n}\rightarrow\infty} \frac{\:\Gamma\:\left(\:\frac{\:{n}+\mathrm{3}}{\mathrm{2}}\:\right)}{{n}^{\:\frac{\mathrm{3}}{\mathrm{2}}} .\Gamma\:\left(\frac{{n}}{\mathrm{2}}\:\right)}\:=\:? \\ $$ Commented by Frix last updated…