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Category: Limits

Question-55491

Question Number 55491 by Tinkutara last updated on 25/Feb/19 Answered by tanmay.chaudhury50@gmail.com last updated on 26/Feb/19 $${trying}\:{to}\:\:{understand}\: \\ $$$${restricting}\:{under}\:{following}\:{condition} \\ $$$$\left.\mathrm{1}\right){radius}\left({r}\right)\:{taken}\:{as}\:{integer} \\ $$$$\left.\mathrm{2}\right){centre}\:{and}\:{otherpoints}\:\boldsymbol{{lie}}\:\boldsymbol{{on}}\:\boldsymbol{{the}}\:\boldsymbol{{circle}} \\ $$$$\boldsymbol{{not}}\:\boldsymbol{{counted}}\:\boldsymbol{{in}}\:\boldsymbol{{f}}\left(\boldsymbol{{r}}\right)…

calculate-lim-x-3-x-1-2-3-x-6-

Question Number 121010 by mathocean1 last updated on 04/Nov/20 $$\mathrm{calculate}: \\ $$$$\underset{\mathrm{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\:\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{2}}{\mathrm{3}−\sqrt{\mathrm{x}+\mathrm{6}}} \\ $$ Answered by 675480065 last updated on 04/Nov/20 $$=\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}+\mathrm{1}}}}{−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}+\mathrm{6}}}}=−\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\sqrt{\frac{\mathrm{x}+\mathrm{6}}{\mathrm{x}+\mathrm{1}}}=−\mathrm{3}/\mathrm{2}…

lim-x-sin-2-2-x-cos-1-x-1-sec-3-x-tan-2-3-x-

Question Number 120862 by bemath last updated on 03/Nov/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2}}{\mathrm{x}}\right)−\mathrm{cos}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{1}}{\mathrm{sec}\:\left(\frac{\mathrm{3}}{\mathrm{x}}\right)\:\mathrm{tan}\:^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{x}}\right)}\:? \\ $$ Commented by liberty last updated on 03/Nov/20 $$\mathrm{take}\:\mathrm{X}=\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{then}\:\:\underset{\mathrm{X}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{2X}−\mathrm{cos}\:\mathrm{X}+\mathrm{1}}{\mathrm{sec}\:\mathrm{3X}.\:\mathrm{tan}\:^{\mathrm{2}}…

lim-x-3-x-9-6-x-x-3-

Question Number 120843 by bramlexs22 last updated on 03/Nov/20 $$\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{9}−\mathrm{6}\sqrt{\mathrm{x}}}}{\:\sqrt{\mathrm{x}}−\mathrm{3}}\:? \\ $$ Commented by Dwaipayan Shikari last updated on 03/Nov/20 $$\frac{\sqrt{\mathrm{12}−\mathrm{6}\sqrt{\mathrm{3}}}}{\:\sqrt{\mathrm{3}}−\mathrm{3}}=−\mathrm{1} \\ $$ Answered…

Question-120823

Question Number 120823 by bramlexs22 last updated on 03/Nov/20 Answered by liberty last updated on 03/Nov/20 $$\:\rho\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{x}^{\mathrm{3}} }}−\mathrm{1}}{\mathrm{xsin}\:\mathrm{x}} \\ $$$$\:\rho=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{x}−\mathrm{1}\right)+\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{x}^{\mathrm{3}} }}{\mathrm{x}\:\mathrm{sin}\:\mathrm{x}}\:.\left(\frac{\mathrm{1}}{\mathrm{2}}\right)…

Given-lim-x-x-2-x-3-x-b-4-find-the-value-of-b-2-1-

Question Number 120720 by bramlexs22 last updated on 02/Nov/20 $$\:\mathrm{Given}\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{x}+\mathrm{2}\sqrt{\mathrm{x}}+\mathrm{3}}\:−\sqrt{\mathrm{x}}+\mathrm{b}\:=\:\mathrm{4} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{b}^{\mathrm{2}} +\mathrm{1} \\ $$ Answered by Dwaipayan Shikari last updated on 02/Nov/20 $$\sqrt{{x}}\left(\sqrt{\mathrm{1}+\frac{\mathrm{2}}{\:\sqrt{{x}}}+\frac{\mathrm{3}}{{x}}}−\mathrm{1}+\frac{{b}}{\:\sqrt{{x}}}\right)=\mathrm{4}…