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AllQuestion and Answers: Page 1106

Question Number 108181 Answers: 0 Comments: 9

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

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

Question Number 108144 Answers: 0 Comments: 0

∫ (√(ln(x)))dx

$$\int\:\sqrt{{ln}\left({x}\right)}{dx} \\ $$

Question Number 108143 Answers: 2 Comments: 0

cos^2 x+cos^2 2x=sin^2 3x Solve the equation. Please help ASAP

$$\mathrm{cos}^{\mathrm{2}} \mathrm{x}+\mathrm{cos}^{\mathrm{2}} \mathrm{2x}=\mathrm{sin}^{\mathrm{2}} \mathrm{3x} \\ $$$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}. \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{ASAP} \\ $$

Question Number 108133 Answers: 2 Comments: 1

Question Number 108131 Answers: 3 Comments: 1

Question Number 108118 Answers: 1 Comments: 0

Question Number 108114 Answers: 1 Comments: 0

Question Number 108107 Answers: 1 Comments: 2

Question Number 108104 Answers: 1 Comments: 0

Question Number 108099 Answers: 3 Comments: 1

((★BeMath⊚)/⊓) (1) ∫ x tan^(−1) (x) dx ? (2) Find the distance of the point (3,3,1) from the plane Π with equation (r^→ −i^→ −j^→ )•(i^→ −j^→ +k^→ ) = 0 , also find the point on the plane that is nearest to (3,3,1).

$$\:\:\:\:\frac{\bigstar\mathcal{B}{e}\mathcal{M}{ath}\circledcirc}{\sqcap} \\ $$$$\:\left(\mathrm{1}\right)\:\int\:{x}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)\:{dx}\:? \\ $$$$\left(\mathrm{2}\right)\:{Find}\:{the}\:{distance}\:{of}\:{the}\:{point}\: \\ $$$$\left(\mathrm{3},\mathrm{3},\mathrm{1}\right)\:{from}\:{the}\:{plane}\:\Pi\:{with}\:{equation} \\ $$$$\left(\overset{\rightarrow} {{r}}−\overset{\rightarrow} {{i}}−\overset{\rightarrow} {{j}}\right)\bullet\left(\overset{\rightarrow} {{i}}−\overset{\rightarrow} {{j}}+\overset{\rightarrow} {{k}}\right)\:=\:\mathrm{0}\:,\:{also}\: \\ $$$${find}\:{the}\:{point}\:{on}\:{the}\:{plane}\:{that}\:{is} \\ $$$${nearest}\:{to}\:\left(\mathrm{3},\mathrm{3},\mathrm{1}\right). \\ $$$$ \\ $$

Question Number 108095 Answers: 3 Comments: 0

((∞BeMath∞)/♠) ∫ 2x cos^(−1) (x) dx

$$\:\:\:\frac{\infty\mathcal{B}{e}\mathcal{M}{ath}\infty}{\spadesuit} \\ $$$$\:\:\:\int\:\mathrm{2}{x}\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)\:{dx}\: \\ $$

Question Number 108085 Answers: 2 Comments: 1

((⋓BeMath⋓)/∞) sin^8 75°−cos^8 75° =

$$\:\:\:\:\:\frac{\Cup\mathcal{B}{e}\mathcal{M}{ath}\Cup}{\infty} \\ $$$$\:\:\:\mathrm{sin}\:^{\mathrm{8}} \mathrm{75}°−\mathrm{cos}\:^{\mathrm{8}} \mathrm{75}°\:= \\ $$

Question Number 108082 Answers: 1 Comments: 0

Question Number 108076 Answers: 0 Comments: 0

can someone please show how to get ∫_0 ^π sin (a sin (x)) dx=πH_0 (a) where H_0 (a) is the Struve−H−Function

$$\mathrm{can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{show}\:\mathrm{how}\:\mathrm{to}\:\mathrm{get} \\ $$$$\underset{\mathrm{0}} {\overset{\pi} {\int}}\mathrm{sin}\:\left({a}\:\mathrm{sin}\:\left({x}\right)\right)\:{dx}=\pi\mathrm{H}_{\mathrm{0}} \:\left({a}\right) \\ $$$$\mathrm{where}\:\mathrm{H}_{\mathrm{0}} \:\left({a}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{Struve}−\mathrm{H}−\mathrm{Function} \\ $$

Question Number 108073 Answers: 3 Comments: 0

((≜BeMath≜)/≺) ∫ ((x dx)/(x^8 −1)) ?

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

Question Number 108071 Answers: 1 Comments: 0

Question Number 108068 Answers: 4 Comments: 0

Question Number 108067 Answers: 2 Comments: 0

Question Number 108059 Answers: 1 Comments: 0

((♥JS♥)/(°js°)) Given a matrix A= ((( 3 2)),((−5 −4)) ) and A^2 +♭A−2I=0 where ♭ is a constant , I= (((1 0)),((0 1)) ). If B = (((−3♭ 2)),(( 5♭ −1)) ) , then A^(−1) B =

$$\:\:\:\frac{\heartsuit{JS}\heartsuit}{°{js}°} \\ $$$${Given}\:{a}\:{matrix}\:{A}=\begin{pmatrix}{\:\:\:\mathrm{3}\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{5}\:\:\:−\mathrm{4}}\end{pmatrix} \\ $$$${and}\:{A}^{\mathrm{2}} +\flat{A}−\mathrm{2}{I}=\mathrm{0}\:{where}\:\flat\:{is}\:{a} \\ $$$${constant}\:,\:{I}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}.\:{If}\:{B}\:= \\ $$$$\begin{pmatrix}{−\mathrm{3}\flat\:\:\:\:\:\:\mathrm{2}}\\{\:\:\:\mathrm{5}\flat\:\:\:\:−\mathrm{1}}\end{pmatrix}\:,\:{then}\:{A}^{−\mathrm{1}} {B}\:=\: \\ $$

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