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Author: Tinku Tara

prove-that-1-itan-i-cot-itan-pleas-sir-help-me-

Question Number 73560 by mhmd last updated on 13/Nov/19 $${prove}\:{that}\:\left(\mathrm{1}−{itan}\theta\right)/\left({i}+{cot}\theta\right)={itan}\theta \\ $$$${pleas}\:{sir}\:{help}\:{me}? \\ $$ Commented by MJS last updated on 13/Nov/19 $$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{generally}\:\mathrm{true} \\ $$$$\frac{\mathrm{1}−\mathrm{i}\:\mathrm{tan}\:\theta}{\mathrm{i}+\mathrm{cot}\:\theta}=\mathrm{2sin}\:\theta\:\mathrm{cos}\:\theta\:−\mathrm{tan}\:\theta\:−\mathrm{2i}\:\mathrm{sin}^{\mathrm{2}} \:\theta…

find-the-value-of-for-which-f-x-2-x-if-x-lt-1-2-x-1-if-x-gt-1-has-a-limit-as-x-1-

Question Number 73561 by Rio Michael last updated on 13/Nov/19 $${find}\:{the}\:{value}\:{of}\:\lambda\:{for}\:{which} \\ $$$$\:{f}\::\:{x}\:\rightarrow\:\begin{cases}{\mathrm{2}\lambda\:−\:{x},\:{if}\:{x}\:<\:\mathrm{1}}\\{\lambda^{\mathrm{2}} \:+\:{x}\:−\mathrm{1},\:{if}\:{x}\:>\:\mathrm{1}}\end{cases} \\ $$$${has}\:{a}\:{limit}\:{as}\:{x}\rightarrow\:\mathrm{1} \\ $$ Answered by ajfour last updated on 13/Nov/19…

find-a-Lim-x-ln-1-e-x-e-x-b-lim-x-x-2-3x-x-c-lim-x-0-x-ln-sinx-d-lim-x-e-2x-1-e-x-x-2-x-1-e-lim-x-1-xe-x-

Question Number 73555 by Rio Michael last updated on 13/Nov/19 $${find}\: \\ $$$$\left.{a}\right)\:\:\underset{{x}\rightarrow−\infty} {{Lim}}\:\frac{{ln}\left(\mathrm{1}+{e}^{{x}} \right)}{{e}^{{x}} } \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow+\infty} {{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{3}{x}}\:\:−{x}\right) \\ $$$$\left.{c}\right)\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\sqrt{{x}}\:{ln}\left({sinx}\right) \\ $$$$\left.{d}\right)\:\:\underset{{x}\rightarrow+\infty}…

give-a-b-c-gt-0-if-a-b-and-b-c-prove-a-c-

Question Number 73553 by 01 last updated on 13/Nov/19 $$\mathrm{give}:\:\mathrm{a},\mathrm{b},\mathrm{c}>\mathrm{0} \\ $$$$\mathrm{if}\:\mathrm{a}\mid\mathrm{b}\:\mathrm{and}\:\mathrm{b}\mid\mathrm{c} \\ $$$$\mathrm{prove}\::\:\mathrm{a}\mid\mathrm{c} \\ $$ Answered by Rio Michael last updated on 13/Nov/19 $${a}\mid{b}\:\Leftrightarrow\:\exists\:{k}\in\mathbb{Z}\::\:\:{b}\:=\:{ka}\:……\left({i}\right)…