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Category: Limits

Question-168911

Question Number 168911 by bagjagugum123 last updated on 21/Apr/22 Commented by infinityaction last updated on 21/Apr/22 $$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\:\frac{\left({x}^{\mathrm{2}} −{a}^{\mathrm{2}} \right)\mathrm{sin}\:\left({x}−{a}\right)\left(\sqrt{{x}+{b}}+\sqrt{{a}+{b}}\right)^{\mathrm{2}} }{\:\left(\sqrt{{x}+{b}}−\sqrt{{a}+{b}}\right)^{\mathrm{2}} \left(\sqrt{{x}+{b}}+\sqrt{{a}+{b}}\right)^{\mathrm{2}} } \\ $$$$\underset{{x}\rightarrow{a}}…

Question-103366

Question Number 103366 by Study last updated on 14/Jul/20 Answered by mathmax by abdo last updated on 14/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\frac{\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{4}}} −\mathrm{5}^{\frac{\mathrm{1}}{\left\{\right.}} }{\left(\mathrm{lnx}\right)^{\frac{\mathrm{1}}{\mathrm{8}}} −\left(\mathrm{ln5}\right)^{\frac{\mathrm{1}}{\mathrm{8}}} }\:\:\mathrm{let}\:\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{5}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{we}\:\mathrm{do}\:\mathrm{the}\:\mathrm{changement} \\…

De-montrer-que-Demonstrate-that-lim-x-0-e-x-1-ln-x-1-cos-x-1-2-

Question Number 168819 by AbdoulayeLelouche last updated on 18/Apr/22 $$\mathrm{D}\acute {\mathrm{e}montrer}\:\mathrm{que}: \\ $$$$\mathrm{Demonstrate}\:\mathrm{that}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{e}^{{x}} −\mathrm{1}−\mathrm{ln}\:\left({x}+\mathrm{1}\right)}{\mathrm{cos}\:\left({x}\right)−\mathrm{1}}\right)\:=\:−\mathrm{2} \\ $$ Answered by alephzero last updated on…

Calculate-lim-x-0-2x-1-2x-1-e-t-2-dt-1-1-e-t-2-dt-x-2-8e-Don-t-use-L-Hospital-s-rule-

Question Number 168696 by qaz last updated on 16/Apr/22 $$\mathrm{Calculate}\:\:\:::\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{2x}−\mathrm{1}} ^{\mathrm{2x}+\mathrm{1}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}−\int_{−\mathrm{1}} ^{\mathrm{1}} \mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \mathrm{dt}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{8e}\:\:\:,\mathrm{Don}'\mathrm{t}\:\mathrm{use}\:\mathrm{L}'\mathrm{Hospital}'\mathrm{s}\:\mathrm{rule}. \\ $$ Answered by aleks041103…

If-lim-x-0-cos-m-mx-cos-n-nx-m-2-n-2-mn-x-2-1-find-m-2-n-2-4-mn-

Question Number 168576 by cortano1 last updated on 13/Apr/22 $$\:\:\:{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:^{{m}} \left({mx}\right)−\mathrm{cos}\:^{{n}} \left({nx}\right)}{\left({m}^{\mathrm{2}} +{n}^{\mathrm{2}} +{mn}\right){x}^{\mathrm{2}} \:}\:=\:\mathrm{1} \\ $$$$\:{find}\:\frac{{m}^{\mathrm{2}} +{n}^{\mathrm{2}} −\mathrm{4}}{{mn}}\:. \\ $$ Commented by blackmamba…