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cos2x-sinx-tg-225-0-360-sum-of-roots-

Question Number 207498 by hardmath last updated on 17/May/24 $$\mathrm{cos2}\boldsymbol{\mathrm{x}}\:+\:\mathrm{sin}\boldsymbol{\mathrm{x}}\:=\:\mathrm{tg}\left(\mathrm{225}°\right)\centerdot\left(\mathrm{0},\mathrm{360}°\right) \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{roots}\:=\:? \\ $$ Answered by MM42 last updated on 17/May/24 $$−\mathrm{2}{sin}^{\mathrm{2}} {x}+{sinx}=\mathrm{0} \\ $$$${sinx}=\mathrm{0}\Rightarrow{x}=\pi…

lim-n-n-1-n-2-n-3-

Question Number 207493 by hardmath last updated on 17/May/24 $$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{n}\:−\:\mathrm{1}}{\mathrm{n}\:+\:\mathrm{2}}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{3}} \:=\:\:? \\ $$ Answered by A5T last updated on 17/May/24 $$\left(\frac{{n}+\mathrm{2}}{{n}−\mathrm{1}}\right)^{{n}+\mathrm{3}} =\left(\frac{{n}−\mathrm{1}+\mathrm{3}}{{n}−\mathrm{1}}\right)^{{n}+\mathrm{3}} =\left(\mathrm{1}+\frac{\mathrm{3}}{{n}−\mathrm{1}}\right)^{{n}+\mathrm{3}} \\…

is-there-any-generale-form-for-this-sequense-u-n-1-au-n-b-cu-n-d-u-m-k-I-need-u-n-in-terms-of-n-i-have-try-to-derrive-it-for-a-long-time-but-i-cant-

Question Number 207477 by AliJumaa last updated on 16/May/24 $${is}\:{there}\:{any}\:{generale}\:{form}\:{for}\:{this}\:{sequense}\: \\ $$$$\begin{cases}{{u}_{{n}+\mathrm{1}} =\frac{{au}_{{n}} +{b}}{{cu}_{{n}} +{d}}}\\{{u}_{{m}} ={k}}\end{cases} \\ $$$${I}\:{need}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n}\:{i}\:{have}\:{try}\:{to}\:{derrive}\:{it}\:{for}\:{a}\:{long}\:{time}\:{but}\:{i}\:{cant} \\ $$ Commented by Frix last…

Question-207461

Question Number 207461 by yaslm last updated on 16/May/24 Commented by mr W last updated on 16/May/24 $${what}\:{do}\:{you}\:{mean}\:{with}\:“{first}\:{go}''? \\ $$$${if}\:{you}\:{mean}\:{which}\:{tank}\:{will}\:{be}\:{filled} \\ $$$${at}\:{first},\:{i}\:{think}\:{it}'{s}\:{the}\:{tank}\:{F}. \\ $$ Commented…

4-sin-x-2-1-find-x-

Question Number 207462 by hardmath last updated on 16/May/24 $$\mathrm{4}\:\mathrm{sin}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:=\:\mathrm{1}\:\:\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Commented by Frix last updated on 16/May/24 $${x}=\mathrm{4}{n}\pi+\mathrm{2sin}^{−\mathrm{1}} \:\frac{\mathrm{1}}{\mathrm{4}}\:\vee{x}=\mathrm{2}\left(\mathrm{2}{n}+\mathrm{1}\right)\pi−\mathrm{2sin}^{−\mathrm{1}} \:\frac{\mathrm{1}}{\mathrm{4}} \\ $$ Terms…

1-sin-2-x-2-find-x-

Question Number 207463 by hardmath last updated on 16/May/24 $$\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{x}\:=\:\sqrt{\mathrm{2}}\:\:\:\:\:\mathrm{find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$ Answered by Frix last updated on 16/May/24 $$\mathrm{cos}^{\mathrm{2}} \:{x}\:=\sqrt{\mathrm{2}}>\mathrm{1}\:\Rightarrow\:\mathrm{no}\:\mathrm{solution}\:\mathrm{for}\:{x}\in\mathbb{R} \\ $$ Terms…