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Author: Tinku Tara

without-L-hopital-lim-x-1-2-2x-3-3x-2-a-bx-4x-2-1-3-4-find-a-b-

Question Number 84568 by jagoll last updated on 14/Mar/20 $$\mathrm{without}\:\mathrm{L}'\mathrm{hopital} \\ $$$$\underset{{x}\rightarrow−\frac{\mathrm{1}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{2x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\sqrt{\mathrm{a}+\mathrm{bx}}}{\mathrm{4x}^{\mathrm{2}} −\mathrm{1}}\:=\:−\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b} \\ $$ Commented by john santu last…

find-arg-z-given-that-z-1-i-1-i-

Question Number 84564 by Rio Michael last updated on 14/Mar/20 $$\mathrm{find}\:\mathrm{arg}\left(\mathrm{z}\right)\:\mathrm{given}\:\mathrm{that}\:\:\mathrm{z}\:=\:\frac{\mathrm{1}\:+\:{i}}{\mathrm{1}−{i}} \\ $$ Commented by mr W last updated on 14/Mar/20 $${z}=\frac{\mathrm{1}+{i}}{\mathrm{1}−{i}}=\frac{\left(\mathrm{1}+{i}\right)\left(\mathrm{1}+{i}\right)}{\mathrm{1}−{i}^{\mathrm{2}} }=\frac{\mathrm{1}+\mathrm{2}{i}+{i}^{\mathrm{2}} }{\mathrm{2}}={i} \\…

Question-150097

Question Number 150097 by mathdanisur last updated on 09/Aug/21 Answered by Kamel last updated on 09/Aug/21 $${u}_{{n}} =\underset{{p}=\mathrm{0}} {\overset{{m}} {\prod}}\gamma_{{n}+{p}} =\left(\gamma+\frac{\mathrm{1}}{\mathrm{2}{n}}\right)^{{m}+\mathrm{1}} +{o}\left(\frac{\mathrm{1}}{{n}}\right)=\gamma^{{m}+\mathrm{1}} +\left({m}+\mathrm{1}\right)\frac{\gamma^{{m}} }{\mathrm{2}{n}}+{o}\left(\frac{\mathrm{1}}{{n}}\right) \\…