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Category: Limits

find-the-values-of-x-for-which-x-3-8-x-2-4-is-discontinuous-and-state-each-kinds-of-dicontinuity-

Question Number 12651 by okhemafrancis last updated on 28/Apr/17 $${find}\:{the}\:{values}\:{of}\:{x}\:{for}\:{which}\:\frac{{x}^{\mathrm{3}} +\mathrm{8}}{{x}^{\mathrm{2}} −\mathrm{4}\:}{is}\:{discontinuous}\:{and}\:{state}\:{each}\:{kinds}\:{of}\:{dicontinuity} \\ $$ Answered by FilupS last updated on 28/Apr/17 $${f}\left({x}\right)=\frac{{x}^{\mathrm{3}} +\mathrm{8}}{{x}^{\mathrm{2}} −\mathrm{4}} \\…

lim-x-x-2-sec-2-x-1-

Question Number 12513 by Joel577 last updated on 24/Apr/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\left[\mathrm{sec}\:\left(\frac{\mathrm{2}}{{x}}\right)\:−\:\mathrm{1}\right] \\ $$ Answered by ajfour last updated on 24/Apr/17 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \left[\frac{\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{2}/{x}\right)}−\mathrm{1}\right] \\…

prove-that-lim-x-1-sin-cos-x-x-1-2-3-2-

Question Number 78012 by malwaan last updated on 13/Jan/20 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{1}} {\boldsymbol{{lim}}}\frac{\boldsymbol{{sin}}\left(\boldsymbol{\pi{cos}\pi{x}}\right)}{\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} }\:=\:−\:\frac{\boldsymbol{\pi}^{\mathrm{3}} }{\mathrm{2}} \\ $$ Commented by msup trace by abdo last updated…

lim-x-0-1-1-x-2-cos-x-tan-4-x-

Question Number 143532 by bramlexs22 last updated on 15/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{cos}\:{x}}{\mathrm{tan}\:^{\mathrm{4}} {x}}\:=? \\ $$ Answered by mathmax by abdo last updated on 15/Jun/21 $$\mathrm{cosx}\sim\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}}…