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Find-a-b-c-which-fulfill-lim-x-0-x-a-b-cos-x-c-sin-x-x-5-1-

Question Number 66544 by naka3546 last updated on 17/Aug/19 $${Find}\:\:{a},\:{b},\:{c}\:\:{which}\:\:{fulfill}\:\:\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{x}\left({a}\:+\:{b}\:\mathrm{cos}\:{x}\right)\:−\:{c}\:\mathrm{sin}\:{x}}{{x}^{\mathrm{5}} }\:\:=\:\:\mathrm{1} \\ $$ Answered by Tanmay chaudhury last updated on 17/Aug/19 $$\underset{{x}\rightarrow\mathrm{0}}…

3-x-3x-x-

Question Number 66543 by hmamarques1994@gmail.com last updated on 17/Aug/19 $$\:\mathrm{3}^{\boldsymbol{{x}}} =\mathrm{3}\boldsymbol{{x}} \\ $$$$\: \\ $$$$\:\boldsymbol{{x}}=? \\ $$ Commented by gunawan last updated on 17/Aug/19 $${x}=\mathrm{1}…

we-say-that-Log-z-1-z-2-Log-z-1-Log-z-2-when-Re-z-1-0-and-Re-z-2-0-prove-this-

Question Number 132032 by mohammad17 last updated on 10/Feb/21 $${we}\:{say}\:{that}\:{Log}\left({z}_{\mathrm{1}} {z}_{\mathrm{2}} \right)={Log}\left({z}_{\mathrm{1}} \right)+{Log}\left({z}_{\mathrm{2}} \right) \\ $$$${when}:\:{Re}\left({z}_{\mathrm{1}} \right)\leqslant\mathrm{0}\:{and}\:{Re}\left({z}_{\mathrm{2}} \right)\leqslant\mathrm{0} \\ $$$${prove}\:{this}\:? \\ $$ Commented by mohammad17…

lim-x-2-log-x-2-1-log-2-1-x-1-

Question Number 66478 by hmamarques1994@gmail.com last updated on 15/Aug/19 $$\: \\ $$$$\:\underset{\boldsymbol{{x}}\rightarrow\mathrm{2}} {\boldsymbol{{lim}}}\left[\frac{\boldsymbol{{log}}_{\boldsymbol{{x}}} \left(\mathrm{2}\right)−\mathrm{1}}{\boldsymbol{{log}}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\boldsymbol{{x}}}\right)+\mathrm{1}}\right]=? \\ $$$$\: \\ $$ Commented by gunawan last updated on…