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Category: Limits

Find-the-lim-x-e-x-e-2x-1-

Question Number 25221 by chernoaguero@gmail.com last updated on 06/Dec/17 $$\mathrm{Find}\:\mathrm{the}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{e}^{\mathrm{x}} }{\:\sqrt{\mathrm{e}^{\mathrm{2x}} +\mathrm{1}}} \\ $$ Answered by jota+ last updated on 06/Dec/17 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\left(\mathrm{1}/{e}^{{x}} \right){e}^{{x}}…

lim-x-0-1-x-1-x-2-2-cos-x-1-

Question Number 90722 by jagoll last updated on 25/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{1}+{x}}\:−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)^{\mathrm{2}} }{\mathrm{cos}\:{x}−\mathrm{1}}\:=\:? \\ $$ Commented by john santu last updated on 25/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\sqrt{\mathrm{1}+{x}}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…

lim-x-0-1-cos-x-cos-2x-cos-3x-1-3-cos-4x-1-4-x-2-

Question Number 156250 by cortano last updated on 09/Oct/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\:\sqrt{\mathrm{cos}\:\mathrm{2x}}\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3x}}\:\sqrt[{\mathrm{4}}]{\mathrm{cos}\:\mathrm{4x}}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$ Commented by john_santu last updated on 09/Oct/21 $${limit}=\frac{\mathrm{4}×\mathrm{5}}{\mathrm{4}}=\mathrm{5} \\ $$ Terms…

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

Question Number 90432 by jagoll last updated on 23/Apr/20 $$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\mathrm{x}\left[\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}−\mathrm{x}\:\right]\:=? \\ $$ Commented by mathmax by abdo last updated on 23/Apr/20 $${we}\:{have}\:{lim}_{{x}\rightarrow−\infty} \:{x}\:=−\infty\:\:{and}…

lim-a-0-1-cos-3a-1-3-cos-2a-cos-a-a-sin-a-cos-2a-

Question Number 155937 by cortano last updated on 06/Oct/21 $$\:\underset{\mathrm{a}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{3a}}\:\sqrt{\mathrm{cos}\:\mathrm{2a}}\:\mathrm{cos}\:\mathrm{a}}{\mathrm{a}\:\mathrm{sin}\:\mathrm{a}\:\mathrm{cos}\:\mathrm{2a}}\:=? \\ $$ Commented by john_santu last updated on 06/Oct/21 $${Limit}\:=\:\mathrm{3} \\ $$ Terms of…

Solve-the-following-trigonometric-limit-lim-x-pi-4-5tg-x-

Question Number 24864 by A1B1C1D1 last updated on 27/Nov/17 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{trigonometric}\:\mathrm{limit}: \\ $$$$ \\ $$$$\underset{\mathrm{x}\:\rightarrow\:\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\left(\mathrm{5tg}\left(\mathrm{x}\right)\right)\:=\: \\ $$ Answered by jota+ last updated on 28/Nov/17 $$\:\underset{{x}\rightarrow\mathrm{0}}…