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Category: Limits

lim-x-0-x-1-1-2x-1-h-2-x-3-5-h-3-2-9-h-7-

Question Number 161361 by cortano last updated on 17/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}+\mathrm{1}}\:+\sqrt[{{h}}]{\mathrm{1}+\mathrm{2}{x}}−\mathrm{2}}{{x}}\:=\:\frac{\mathrm{3}}{\mathrm{5}}\: \\ $$$$\:\:{h}^{\mathrm{3}} −\frac{\mathrm{2}}{\mathrm{9}}\left({h}+\mathrm{7}\right)=? \\ $$ Commented by vietanhdz last updated on 17/Dec/21 $$\sqrt{{x}+\mathrm{1}}−\mathrm{1}\sim\frac{{x}}{\mathrm{2}}\:{if}\:{x}\sim\mathrm{0} \\…

Find-lim-n-cos-n-2pi-n-

Question Number 30282 by Tinkutara last updated on 19/Feb/18 $${Find}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}cos}^{{n}} \:\left(\frac{\mathrm{2}\pi}{{n}}\right) \\ $$ Commented by prof Abdo imad last updated on 20/Feb/18 $${we}\:{have}\:\:{cosx}\:\sim\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:{for}\:{x}\in{v}\left(\mathrm{0}\right)\Rightarrow…

1-lim-x-0-2cos-p-x-cos-p-2x-cos-p-x-2-2-lim-x-0-tan-2x-q-2tan-x-q-tan-q-x-2-

Question Number 161337 by bobhans last updated on 16/Dec/21 $$\:\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2cos}\:\left(\mathrm{p}+\mathrm{x}\right)−\mathrm{cos}\:\left(\mathrm{p}+\mathrm{2x}\right)−\mathrm{cos}\:\mathrm{p}}{\mathrm{x}^{\mathrm{2}} }\:? \\ $$$$\:\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{2x}+\mathrm{q}\right)−\mathrm{2tan}\:\left(\mathrm{x}+\mathrm{q}\right)+\mathrm{tan}\:\mathrm{q}}{\mathrm{x}^{\mathrm{2}} }\:? \\ $$ Commented by cortano last updated on 16/Dec/21…

lim-x-pi-2-cos-x-sin-x-cos-x-1-3-sin-x-

Question Number 161319 by cortano last updated on 16/Dec/21 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}}{\:\sqrt[{\mathrm{3}}]{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}−\mathrm{sin}\:{x}}=? \\ $$ Answered by som(math1967) last updated on 16/Dec/21 $$\underset{\boldsymbol{{x}}\rightarrow\frac{\boldsymbol{\pi}}{\mathrm{2}}} {\boldsymbol{{lim}}}\:\frac{\boldsymbol{{cosx}}\left\{\left(\boldsymbol{{sinx}}+\boldsymbol{{cosx}}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +\left(\boldsymbol{{sinx}}+\boldsymbol{{cosx}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \boldsymbol{{sinx}}+\boldsymbol{{sin}}^{\mathrm{2}} \boldsymbol{{x}}\right\}}{\boldsymbol{{sinx}}+\boldsymbol{{cosx}}−\boldsymbol{{sin}}^{\mathrm{3}}…