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Category: Limits

lim-x-a-2x-a-3x-x-3a-2-x-a-0-

Question Number 104655 by bobhans last updated on 23/Jul/20 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{\sqrt{\mathrm{2}{x}+{a}}−\sqrt{\mathrm{3}{x}}}{\:\sqrt{{x}+\mathrm{3}{a}}−\mathrm{2}\sqrt{{x}}}\:=?\:\:\:\:\left[{a}\neq\mathrm{0}\right]\: \\ $$ Answered by bramlex last updated on 23/Jul/20 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\:\frac{\left[\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{x}+{a}}}−\frac{\mathrm{3}}{\mathrm{2}\sqrt{\mathrm{3}{x}}}\right]}{\left[\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}+\mathrm{3}{a}}}−\frac{\mathrm{1}}{\:\sqrt{{x}}}\right]}\:=\:\frac{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}{a}}}−\frac{\mathrm{3}}{\mathrm{2}\sqrt{\mathrm{3}{a}}}}{\frac{\mathrm{1}}{\mathrm{4}\sqrt{{a}}}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{{a}}}} \\ $$$$=\:\left\{\frac{\mathrm{2}}{\mathrm{2}\sqrt{\mathrm{3}{a}}}−\frac{\mathrm{3}}{\mathrm{2}\sqrt{\mathrm{3}{a}}}\:\right\}×\:\left(−\mathrm{4}\sqrt{{a}}\:\right) \\…

lim-x-0-x-sin-1-x-

Question Number 170182 by mathlove last updated on 18/May/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[{x}\centerdot{sin}\frac{\mathrm{1}}{{x}}\right]=? \\ $$ Commented by mr W last updated on 18/May/22 $${has}\:\left[\:\:\right]\:{special}\:{meaning}?\:{or}\:{you}\:{just}\:{mean} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left({x}\centerdot{sin}\frac{\mathrm{1}}{{x}}\right)=?…

lim-x-4-e-x-24-x-2-

Question Number 170159 by mathlove last updated on 17/May/22 $$\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\:\frac{{e}\:!{x}−\mathrm{24}}{\:\sqrt{{x}}−\mathrm{2}}=? \\ $$ Answered by Mathspace last updated on 18/May/22 $${hosital}\:\:{lim}={lim}_{{x}\rightarrow\mathrm{4}} \:\:\:\frac{{e}!}{\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}} \\ $$$$={lim}_{{x}\rightarrow\mathrm{4}} \:\mathrm{2}\left({e}\right)!\sqrt{{x}}…

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

Question Number 170141 by sciencestudent last updated on 17/May/22 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\left(\frac{\mathrm{1}}{{sin}^{\mathrm{2}} {x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)=? \\ $$ Commented by mr W last updated on 17/May/22 $$=\left(\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{{x}}\right)\left(\frac{\mathrm{1}}{\mathrm{sin}\:{x}}−\frac{\mathrm{1}}{{x}}\right) \\…

lim-x-0-x-1-x-1-x-

Question Number 104606 by john santu last updated on 22/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{{x}−\mathrm{1}}{\mid{x}−\mathrm{1}\mid}\:+\:\mid{x}\mid\right\}=? \\ $$ Answered by bobhans last updated on 22/Jul/20 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left\{\frac{{x}−\mathrm{1}}{\mid{x}−\mathrm{1}\mid}\:+\:\mid{x}\mid\:\right\}\:=\:\underset{{x}\rightarrow\mathrm{0}^{+} }…

Question-39067

Question Number 39067 by bshahid010@gmail.com last updated on 02/Jul/18 Commented by math khazana by abdo last updated on 03/Jul/18 $$={lim}_{{h}\rightarrow\mathrm{0}} \:\:\frac{\mathrm{2}{h}\:−{h}^{\mathrm{3}} \sqrt{\mathrm{8}+{h}}}{\mathrm{2}{h}^{\mathrm{4}} \sqrt{\mathrm{8}+{h}}} \\ $$$$={lim}_{{h}\rightarrow\mathrm{0}}…