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Category: Limits

solve-lim-x-0-x-2-tan-sinpix-2x-solution-let-L-lim-x-0-x-2-tan-sinpix-2x-since-sinx-x-x-3-6-L-lim-x-0-x-2-tan-pix-2x-pi-3-x-3-12x-L-lim-x-0-x-2-tan-pi-2-pi-3-x-2

Question Number 192573 by senestro last updated on 21/May/23 $${solve}; \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}^{\mathrm{2}} {tan}\left(\frac{{sin}\pi{x}}{\mathrm{2}{x}}\right) \\ $$$${solution} \\ $$$${let}\:{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}^{\mathrm{2}} {tan}\left(\frac{{sin}\pi{x}}{\mathrm{2}{x}}\right) \\ $$$${since}\:{sinx}\sim{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}\: \\ $$$${L}=\underset{{x}\rightarrow\mathrm{0}}…

lim-x-0-x-2-tan-sin-pix-2x-

Question Number 192549 by cortano12 last updated on 20/May/23 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{\mathrm{sin}\:\pi\mathrm{x}}{\mathrm{2x}}\right)\:=? \\ $$ Answered by horsebrand11 last updated on 20/May/23 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\mathrm{tan}\:\left(\frac{\mathrm{sin}\:\pi{x}}{\mathrm{2}{x}}\right) \\…

f-x-y-2x-x-2-y-2-x-2-y-2-x-y-0-0-0-x-y-0-0-check-continuity-

Question Number 127009 by BHOOPENDRA last updated on 26/Dec/20 $${f}\left({x},{y}\right)=\left\{\frac{\mathrm{2}{x}\left({x}^{\mathrm{2}} −{y}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:\:\:\:,\left({x},{y}\right)\neq\left(\mathrm{0},\mathrm{0}\right)\right. \\ $$$$\left\{\mathrm{0}\:\:\:\:,\left({x},{y}\right)=\left(\mathrm{0},\mathrm{0}\right)\right. \\ $$$${check}\:{continuity} \\ $$ Answered by Olaf last updated…

lim-x-0-1-cos-ln-3x-1-3x-6-tan-3x-2-

Question Number 192433 by cortano12 last updated on 18/May/23 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{ln}\:\left(\mathrm{3x}+\mathrm{1}\right)\right)}{\mathrm{3x}^{\mathrm{6}} −\mathrm{tan}\:\left(\mathrm{3x}^{\mathrm{2}} \right)}=? \\ $$ Answered by mehdee42 last updated on 18/May/23 $${tip}\::{if}\:\:{u}\rightarrow\mathrm{0} \\ $$$$\Rightarrow\mathrm{1}−{cosu}\sim\frac{\mathrm{1}}{\mathrm{2}}{u}^{\mathrm{2}}…