Menu Close

Category: Limits

Question-142041

Question Number 142041 by nadovic last updated on 25/May/21 Answered by TheSupreme last updated on 25/May/21 $$\sqrt{−\mathrm{3}{a}+{b}}−\mathrm{2}=\mathrm{0} \\ $$$${b}−\mathrm{3}{a}=\mathrm{4} \\ $$$$\frac{−\mathrm{3}{a}}{\mathrm{2}\sqrt{−\mathrm{3}{a}+{b}}}=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{6}{a}=\sqrt{−\mathrm{3}{a}+{b}} \\ $$$$\mathrm{36}{a}^{\mathrm{2}}…

find-lim-x-0-log-x-n-x-x-n-N-where-x-represents-greatest-integer-less-than-or-equal-to-x-

Question Number 141966 by gsk2684 last updated on 25/May/21 $${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{log}\:{x}^{{n}} −\left[{x}\right]}{\left[{x}\right]},\:{n}\in{N}\:{where}\: \\ $$$$\left[{x}\right]\:{represents}\:{greatest}\:{integer}\:{less}\:{than}\:{or}\:{equal}\:{to}\:{x}. \\ $$ Commented by gsk2684 last updated on 25/May/21 $${solution}\:{please} \\…

prove-that-0-pi-x-sin-x-1-2-dx-pi-8-2-1-4-

Question Number 141914 by mnjuly1970 last updated on 24/May/21 $$\:\:\:\: \\ $$$$\:\:\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\phi:=\int_{\mathrm{0}} ^{\:\pi} \frac{{x}}{\left({sin}\left({x}\right)\right)^{\frac{\mathrm{1}}{\mathrm{2}}} }{dx}=\sqrt{\frac{\pi}{\mathrm{8}}}\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{4}}\right)…\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:……… \\ $$ Answered by qaz…

Question-141901

Question Number 141901 by gsk2684 last updated on 24/May/21 Commented by gsk2684 last updated on 24/May/21 $${does}\:{this}\:{series}\:{converges}\:{or}\:{diverges} \\ $$$${by}\:{using}\:{comparison}\:{test}\:{or}\:{limit} \\ $$$${comparison}\:{test}?\:{explanation}\:{please} \\ $$ Terms of…

L-lim-x-0-e-x-cos-x-x-1-x-3-

Question Number 141900 by iloveisrael last updated on 24/May/21 $$\:\mathcal{L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{{x}} \:\mathrm{cos}\:{x}−{x}−\mathrm{1}}{{x}^{\mathrm{3}} }\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 24/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{{x}}…

lim-x-3-x-3-x-3-x-3-x-

Question Number 10830 by Saham last updated on 26/Feb/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}^{\mathrm{x}} \:−\:\mathrm{3}^{−\mathrm{x}} }{\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{3}^{−\mathrm{x}} } \\ $$ Answered by bahmanfeshki last updated on 26/Feb/17 $$\underset{{x}\rightarrow\infty}…