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Category: Limits

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

Question Number 168166 by cortano1 last updated on 05/Apr/22 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)−{x}\:\sqrt[{\mathrm{3}}]{\mathrm{1}−{x}}}{{x}^{\mathrm{5}} }\:=? \\ $$ Answered by qaz last updated on 05/Apr/22 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{x}\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{x}}}{\mathrm{x}^{\mathrm{5}} } \\…

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

Question Number 168144 by cortano1 last updated on 04/Apr/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{3}} \sqrt{\mathrm{1}+{x}}\:−\mathrm{sin}\:^{\mathrm{3}} {x}\:−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{3}} \:\mathrm{tan}\:{x}}{\left(\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{2}{x}^{\mathrm{3}} }−\mathrm{1}\right)\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}=?\:\:\:\:\:\:\:\: \\ $$ Answered by qaz last updated on 05/Apr/22…

lim-x-0-1-cos-1-cos-x-x-4-

Question Number 168143 by cortano1 last updated on 04/Apr/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:{x}\right)}{{x}^{\mathrm{4}} }\:=?\:\:\:\:\:\: \\ $$ Answered by qaz last updated on 04/Apr/22 $$ \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}}…

Calculate-lim-x-0-1-x-1-x-3-x-

Question Number 168055 by qaz last updated on 01/Apr/22 $$\mathrm{Calculate}\:::\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+\mathrm{x}\right)^{−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }} }{\mathrm{x}}=? \\ $$ Answered by LEKOUMA last updated on 03/Apr/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\left(\left(\mathrm{1}+{x}\right)−\mathrm{1}\right)\frac{\mathrm{1}}{{x}^{\mathrm{3}} }}…

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

Question Number 102510 by Study last updated on 09/Jul/20 $${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{sin}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{3}}{x}+\frac{\mathrm{1}}{\mathrm{3}}\bigtriangleup{x}\right)−{sin}^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{3}}{x}}{\bigtriangleup{x}}=? \\ $$ Answered by bemath last updated on 09/Jul/20 $$\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{3}}\left({x}+\Delta{x}\right)−\mathrm{sin}\:^{\mathrm{2}}…

lim-x-0-e-sin-x-x-e-sinx-x-

Question Number 102508 by Study last updated on 09/Jul/20 $${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{{sin}\left({x}−\bigtriangleup{x}\right)} −{e}^{{sinx}} }{\bigtriangleup{x}}=? \\ $$ Commented by bemath last updated on 09/Jul/20 $${may}\:{be}\:\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{sin}\:\left({x}+\Delta{x}\right)} −{e}^{\mathrm{sin}\:{x}}…

lim-n-2-2-3-2-5-2-n-1-3-2-3-4-3-n-1-n-2-1-4-

Question Number 36969 by rahul 19 last updated on 07/Jun/18 $$\left[\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}.\mathrm{2}^{\mathrm{3}} .\mathrm{2}^{\mathrm{5}} …..\mathrm{2}^{\mathrm{n}−\mathrm{1}} .\mathrm{3}^{\mathrm{2}} .\mathrm{3}^{\mathrm{4}} …..\mathrm{3}^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}}} \right]^{\mathrm{4}} =? \\ $$ Answered by…