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Question Number 93064 Answers: 1 Comments: 7

prove that (d/dx)x^n =nx^(n−1)

$${prove}\:{that}\: \\ $$$$\frac{{d}}{{dx}}{x}^{{n}} ={nx}^{{n}−\mathrm{1}} \\ $$

Question Number 93061 Answers: 0 Comments: 3

∫_1 ^(+∞) ((sin u)/u)du

$$\int_{\mathrm{1}} ^{+\infty} \frac{\mathrm{sin}\:\mathrm{u}}{\mathrm{u}}\mathrm{du} \\ $$

Question Number 93059 Answers: 1 Comments: 0

y^′ +2xy=cos x+2x sin x

$$\mathrm{y}^{'} +\mathrm{2xy}=\mathrm{cos}\:\mathrm{x}+\mathrm{2x}\:\mathrm{sin}\:\mathrm{x} \\ $$

Question Number 93057 Answers: 1 Comments: 1

y=b1x1+b2x2+c i need to arrange the equation for thd value of x2

$${y}={b}\mathrm{1}{x}\mathrm{1}+{b}\mathrm{2}{x}\mathrm{2}+{c} \\ $$$${i}\:{need}\:{to}\:{arrange}\:{the}\:{equation}\:{for}\:{thd}\:{value}\:{of}\:{x}\mathrm{2} \\ $$

Question Number 93045 Answers: 1 Comments: 2

∫ sin^(−1) ((√(x/2))) dx

$$\int\:\mathrm{sin}^{−\mathrm{1}} \left(\sqrt{\frac{{x}}{\mathrm{2}}}\right)\:{dx}\: \\ $$

Question Number 93044 Answers: 1 Comments: 2

is (8/9) is the multiplicative inerse of −1 (1/8)? why or why not?

$$\mathrm{is}\:\frac{\mathrm{8}}{\mathrm{9}}\:\mathrm{is}\:\mathrm{the}\:\mathrm{multiplicative}\:\mathrm{inerse}\:\mathrm{of}\:−\mathrm{1}\:\frac{\mathrm{1}}{\mathrm{8}}? \\ $$$$\mathrm{why}\:\mathrm{or}\:\mathrm{why}\:\mathrm{not}? \\ $$

Question Number 93039 Answers: 0 Comments: 1

{ ((xy+yz = 8)),((yz+xz = 9)),((zx+xy = 5)) :}

$$\begin{cases}{{xy}+{yz}\:=\:\mathrm{8}}\\{{yz}+{xz}\:=\:\mathrm{9}}\\{{zx}+{xy}\:=\:\mathrm{5}}\end{cases} \\ $$

Question Number 93038 Answers: 1 Comments: 1

∫_1 ^5 (√(x^3 +1)) dx = ?

$$\underset{\mathrm{1}} {\overset{\mathrm{5}} {\int}}\:\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$

Question Number 93033 Answers: 0 Comments: 3

lim_(x→π/6) (tan (((3x)/2)))^(tan (3x)) =?

$$\underset{{x}\rightarrow\pi/\mathrm{6}} {\mathrm{lim}}\:\left(\mathrm{tan}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)\right)^{\mathrm{tan}\:\left(\mathrm{3x}\right)} =?\: \\ $$

Question Number 93031 Answers: 1 Comments: 11

Question Number 93077 Answers: 1 Comments: 1

Se f((√x) −1) = x+6, log[f(1)] = ?

$$\:\:\mathrm{Se}\:\:\mathrm{f}\left(\sqrt{\mathrm{x}}\:−\mathrm{1}\right)\:=\:\mathrm{x}+\mathrm{6},\:\:\mathrm{log}\left[\mathrm{f}\left(\mathrm{1}\right)\right]\:=\:? \\ $$

Question Number 93081 Answers: 0 Comments: 3

Solve x^y =y^x x, y ∈ N

$$\mathrm{Solve}\:\mathrm{x}^{\mathrm{y}} =\mathrm{y}^{\mathrm{x}} \:\:\:\mathrm{x},\:\mathrm{y}\:\in\:\mathbb{N} \\ $$

Question Number 93005 Answers: 1 Comments: 0

∫ sec x (√(sec x+tan x)) dx =

$$\int\:\mathrm{sec}\:\mathrm{x}\:\sqrt{\mathrm{sec}\:\mathrm{x}+\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}\:=\: \\ $$

Question Number 93003 Answers: 1 Comments: 0

(x^2 −2xy−y^2 )dx−(x−y)^2 dy=0

$$\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2xy}−\mathrm{y}^{\mathrm{2}} \right)\mathrm{dx}−\left(\mathrm{x}−\mathrm{y}\right)^{\mathrm{2}} \:\mathrm{dy}=\mathrm{0} \\ $$

Question Number 92997 Answers: 1 Comments: 0

Question Number 92993 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((cos(cosx−sinx))/(x^2 +4))dx

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({cosx}−{sinx}\right)}{{x}^{\mathrm{2}} \:+\mathrm{4}}{dx} \\ $$

Question Number 92987 Answers: 2 Comments: 0

{ (((√y) + ln (x^2 )=2)),((y + 4 ln(x) =28)) :}

$$\begin{cases}{\sqrt{\mathrm{y}}\:+\:\mathrm{ln}\:\left(\mathrm{x}^{\mathrm{2}} \right)=\mathrm{2}}\\{\mathrm{y}\:+\:\mathrm{4}\:\mathrm{ln}\left(\mathrm{x}\right)\:=\mathrm{28}}\end{cases} \\ $$

Question Number 93004 Answers: 0 Comments: 0

∫ ((sin^(−1) (sin (x)))/(sin^4 (x)+cos^2 (x))) dx ?

$$\int\:\frac{\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{sin}\:\left(\mathrm{x}\right)\right)}{\mathrm{sin}\:^{\mathrm{4}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{2}} \left(\mathrm{x}\right)}\:\mathrm{dx}\:? \\ $$

Question Number 92980 Answers: 1 Comments: 0

log _((9x))^(1/(3 )) ((√(x^3 /3))) + log _((3x^2 ))^(1/(3 )) ((√(27x))) ≤ 3

$$\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{9}{x}}} \:\left(\sqrt{\frac{{x}^{\mathrm{3}} }{\mathrm{3}}}\right)\:+\:\mathrm{log}\:_{\sqrt[{\mathrm{3}\:\:}]{\mathrm{3}{x}^{\mathrm{2}} }} \left(\sqrt{\mathrm{27}{x}}\right)\:\leqslant\:\mathrm{3} \\ $$

Question Number 92976 Answers: 1 Comments: 0

define Δ_n =((n(1+n))/2) find a closer form for Σ_(n=1) ^∞ (1/Δ_n ^m )

$${define} \\ $$$$\Delta_{{n}} =\frac{{n}\left(\mathrm{1}+{n}\right)}{\mathrm{2}} \\ $$$${find}\:{a}\:{closer}\:{form}\:{for} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\Delta_{{n}} ^{{m}} } \\ $$

Question Number 92971 Answers: 0 Comments: 3

1) decompose F(x) =(1/(x^4 (x−3)^5 )) 2)calculate ∫_5 ^(+∞) (dx/(x^4 (x−3)^5 ))

$$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{5}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{4}} \left({x}−\mathrm{3}\right)^{\mathrm{5}} } \\ $$

Question Number 92966 Answers: 0 Comments: 3

lim_(x→−∞) ((6x+5)/(√(9x^2 +4x−2))) ?

$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{6x}+\mathrm{5}}{\sqrt{\mathrm{9x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{2}}}\:? \\ $$

Question Number 92960 Answers: 2 Comments: 0

∫ ((sin^2 x dx)/((1+cos x)^2 ))

$$\int\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }\: \\ $$

Question Number 92957 Answers: 0 Comments: 12

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Question Number 92952 Answers: 0 Comments: 1

∫_(−2) ^2 x^3 (cos((x/2))+(1/2))(√(4−x^2 )) dx

$$\int_{−\mathrm{2}} ^{\mathrm{2}} {x}^{\mathrm{3}} \left({cos}\left(\frac{{x}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 92949 Answers: 1 Comments: 2

∫(1/x)sin((1/x)) dx

$$\int\frac{\mathrm{1}}{\mathrm{x}}\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:\mathrm{dx} \\ $$

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