Question and Answers Forum

strange behavior in editor: when you have written for example ((12)/(13)) and you want to delete 13 and change to 24, it is not possible. this occurs also in other cases.

$${strange}\:{behavior}\:{in}\:{editor}: \\ $$$${when}\:{you}\:{have}\:{written}\:{for}\:{example} \\ $$$$\frac{\mathrm{12}}{\mathrm{13}}\:{and}\:{you}\:{want}\:{to}\:{delete}\:\mathrm{13}\:{and} \\ $$$${change}\:{to}\:\mathrm{24},\:{it}\:{is}\:{not}\:{possible}. \\ $$$${this}\:{occurs}\:{also}\:{in}\:{other}\:{cases}. \\ $$

Question Number 108180 Answers: 0 Comments: 0

Solve for u and v in the system of equations below { ((u′(e^(−2x) cos2x)+v′(e^(−2x) sin2x)=0)),((u′(e^(−2x) cos2x)′+v′(e^(−2x) sin2x)′=xe^(−2x) sinx)) :} where u and v are functions of x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:\mathrm{in}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\:\mathrm{below} \\ $$$$\begin{cases}{\mathrm{u}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{cos2x}\right)+\mathrm{v}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{sin2x}\right)=\mathrm{0}}\\{\mathrm{u}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{cos2x}\right)'+\mathrm{v}'\left(\mathrm{e}^{−\mathrm{2x}} \mathrm{sin2x}\right)'=\mathrm{xe}^{−\mathrm{2x}} \mathrm{sinx}}\end{cases} \\ $$$$\mathrm{where}\:\mathrm{u}\:\mathrm{and}\:\mathrm{v}\:\mathrm{are}\:\mathrm{functions}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 108175 Answers: 1 Comments: 3

Question Number 108171 Answers: 1 Comments: 0

If x,y∈R x^2 −xy+4=0 ax^2 +(b+y^2 )x+4a=0 Find the minimum of a^2 +(1/2)b^2

$$\mathrm{If}\:{x},{y}\in\mathbb{R} \\ $$$${x}^{\mathrm{2}} −{xy}+\mathrm{4}=\mathrm{0} \\ $$$${ax}^{\mathrm{2}} +\left({b}+{y}^{\mathrm{2}} \right){x}+\mathrm{4}{a}=\mathrm{0} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{of}\:{a}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}{b}^{\mathrm{2}} \\ $$

Question Number 108169 Answers: 1 Comments: 0

((✓BeMath✓)/(≻≺)) ∫ ((x^5 −x)/(x^8 −1)) dx ?

$$\:\:\:\:\:\:\frac{\checkmark\mathcal{B}{e}\mathcal{M}{ath}\checkmark}{\succ\prec} \\ $$$$\int\:\frac{{x}^{\mathrm{5}} −{x}}{{x}^{\mathrm{8}} −\mathrm{1}}\:{dx}\:? \\ $$

Question Number 108162 Answers: 1 Comments: 0

Question Number 108158 Answers: 1 Comments: 1

test for edit post. edited

$$\mathrm{test}\:\mathrm{for}\:\mathrm{edit}\:\mathrm{post}. \\ $$$${edited} \\ $$

Question Number 108145 Answers: 3 Comments: 2

((⊚BeMath⊚)/Π) (1) cos^2 ((x/4)) > ((√2)/2) + sin^2 ((x/4)) (2) ∫ (√((1+x)/(1−x))) dx (3) ∫_0 ^(π/2) ((√(tan x))/((cos x+sin x)^2 )) dx

$$\:\:\:\frac{\circledcirc\mathcal{B}{e}\mathcal{M}{ath}\circledcirc}{\Pi} \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\mathrm{cos}\:^{\mathrm{2}} \left(\frac{{x}}{\mathrm{4}}\right)\:>\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\:+\:\mathrm{sin}\:^{\mathrm{2}} \left(\frac{{x}}{\mathrm{4}}\right)\: \\ $$$$\:\left(\mathrm{2}\right)\:\int\:\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx} \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\left(\mathrm{cos}\:{x}+\mathrm{sin}\:{x}\right)^{\mathrm{2}} }\:{dx} \\ $$

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