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Category: Limits

lim-x-0-1-x-2-1-3-1-2x-1-4-x-x-2-lim-x-1-7-x-2-1-3-3-x-2-x-1-

Question Number 143064 by EDWIN88 last updated on 09/Jun/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:−\sqrt[{\mathrm{4}}]{\mathrm{1}−\mathrm{2x}}}{\mathrm{x}+\mathrm{x}^{\mathrm{2}} }\:=? \\ $$$$\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{\mathrm{7}+\mathrm{x}^{\mathrm{2}} }−\sqrt{\mathrm{3}+\mathrm{x}^{\mathrm{2}} }}{\mathrm{x}−\mathrm{1}}\:=? \\ $$ Answered by bramlexs22 last updated…

lim-x-1-sin-x-1-2x-x-2-3-

Question Number 142922 by mathlove last updated on 07/Jun/21 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}+\mathrm{1}\right)}{\mathrm{2}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}}=? \\ $$ Answered by Olaf_Thorendsen last updated on 07/Jun/21 $$\frac{\mathrm{sin}\left({x}+\mathrm{1}\right)}{\mathrm{2}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}}\:=\:\frac{\mathrm{sin}\left({x}+\mathrm{1}\right).\left(\mathrm{2}{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}\right)}{\mathrm{4}{x}^{\mathrm{2}} −\left({x}^{\mathrm{2}}…

Question-77234

Question Number 77234 by TawaTawa last updated on 04/Jan/20 Answered by mr W last updated on 04/Jan/20 $$=\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}} {x}^{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{1}}{\mathrm{3}}×\frac{\mathrm{1}}{\mathrm{4}}×\frac{\mathrm{1}}{\mathrm{5}}} …{dx} \\…

Question-142745

Question Number 142745 by iloveisrael last updated on 05/Jun/21 Commented by MJS_new last updated on 05/Jun/21 $$\mathrm{vr}×\mathrm{th7gr}\:\mathrm{bl}\theta\mathrm{p}\:\mathrm{njk}\Pi\mathrm{y}\notin\mathrm{m}\:\mathrm{trf}\digamma\mathrm{sh5jk}\:\left[\spadesuit>{bkl}\right. \\ $$ Commented by iloveisrael last updated on…