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Category: Limits

Determine-i-a-ii-a-in-case-a-a-R-b-a-R-

Question Number 28408 by Rasheed.Sindhi last updated on 25/Jan/18 $$\mathrm{Determine}\:\left(\mathrm{i}\right)\:\frac{\infty}{{a}}\:\:\left(\mathrm{ii}\right)\:\frac{−\infty}{{a}}\:\mathrm{in}\:\mathrm{case}\: \\ $$$$\left({a}\right)\:{a}\in\mathbb{R}^{−} \:\:\:\:\left({b}\right)\:\:{a}\in\mathbb{R}^{+} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

lim-x-0-k-1-2021-k-x-2021-1-x-

Question Number 159405 by qaz last updated on 16/Nov/21 $$\underset{\mathrm{x}\rightarrow+\mathrm{0}} {\mathrm{lim}}\left(\frac{\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{2021}} {\sum}}\mathrm{k}^{\mathrm{x}} }{\mathrm{2021}}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} =? \\ $$ Answered by mindispower last updated on 16/Nov/21 $$=\underset{{x}\rightarrow\mathrm{0}}…

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

Question Number 159395 by cortano last updated on 16/Nov/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{{n}}]{\mathrm{cos}\:\mathrm{2}{x}}}{{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\:{n}=? \\ $$ Answered by qaz last updated on 16/Nov/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt[{\mathrm{n}}]{\mathrm{cos}\:\mathrm{2x}}}{\mathrm{x}^{\mathrm{2}}…

lim-x-1-x-2-1-2-x-2-4-3-x-2-9-

Question Number 159388 by amin96 last updated on 16/Nov/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{2}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{4}}+\frac{\mathrm{3}}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{9}}+\ldots\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-93824

Question Number 93824 by student work last updated on 15/May/20 Answered by john santu last updated on 15/May/20 $$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{lny}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{tan}\:\left(\mathrm{3t}+\frac{\pi}{\mathrm{2}}\right)\mathrm{ln}\left(\mathrm{tan}\:\left(\frac{\mathrm{3t}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)\right) \\ $$$$=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{tan}\:\left(\frac{\mathrm{3t}}{\mathrm{2}}+\frac{\pi}{\mathrm{4}}\right)\right)}{\mathrm{cot}\:\left(\mathrm{3t}+\frac{\pi}{\mathrm{2}}\right)} \\…

lim-x-0-8sec-x-8-tan-4-x-4tan-2-x-x-6-

Question Number 159349 by cortano last updated on 15/Nov/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{8sec}\:{x}−\mathrm{8}+\mathrm{tan}\:^{\mathrm{4}} {x}−\mathrm{4tan}\:^{\mathrm{2}} {x}}{{x}^{\mathrm{6}} }\:=? \\ $$ Commented by bobhans last updated on 16/Nov/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{8}\left(\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}}…

lim-x-1-x-1-x-2-1-x-3-1-x-1-x-2-1-x-4-1-

Question Number 159318 by tounghoungko last updated on 15/Nov/21 $$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{{x}+\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}−\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}}{\:\sqrt{{x}−\mathrm{1}}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:−\sqrt{{x}^{\mathrm{4}} +\mathrm{1}}}\:=? \\ $$ Commented by bobhans last updated on 16/Nov/21 $$\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+}…