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Question Number 134871 Answers: 0 Comments: 0

What is f(x)? such that (f(x)+f ′(x)ln x)ln x=−1

$$\mathrm{What}\:\mathrm{is}\:{f}\left({x}\right)? \\ $$$$\mathrm{such}\:\mathrm{that}\:\left({f}\left({x}\right)+{f}\:'\left({x}\right)\mathrm{ln}\:{x}\right)\mathrm{ln}\:{x}=−\mathrm{1} \\ $$

Question Number 134866 Answers: 2 Comments: 0

let U_n =∫_0 ^∞ ((cos(nx))/((x^2 +n^2 )^2 ))dx calculate lim_(n→+∞) e^n^2 U_n

$$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}\left(\mathrm{nx}\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{n}^{\mathrm{2}} \right)^{\mathrm{2}} }\mathrm{dx}\:\mathrm{calculate}\:\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \mathrm{e}^{\mathrm{n}^{\mathrm{2}} } \mathrm{U}_{\mathrm{n}} \\ $$

Question Number 134858 Answers: 3 Comments: 0

Question Number 134852 Answers: 2 Comments: 0

...nice calculus... find ::: 𝛗=∫_0 ^( 1) ((ln(x)ln(1−x))/(x(1−x)))dx=?

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{nice}\:\:\:\:{calculus}... \\ $$$$\:\:\:\:\:\:{find}\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}\left({x}\right){ln}\left(\mathrm{1}−{x}\right)}{{x}\left(\mathrm{1}−{x}\right)}{dx}=? \\ $$$$ \\ $$

Question Number 134848 Answers: 3 Comments: 2

Question Number 134846 Answers: 0 Comments: 0

Question Number 134845 Answers: 1 Comments: 0

advanced calculus... ∫_0 ^( 1) xψ(1+x)dx=?? ...m.n...

$$\:\:\:\:\:\:\:\:\:\:\:{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\psi\left(\mathrm{1}+{x}\right){dx}=?? \\ $$$$\:\:\:\:\:\:\:\:...{m}.{n}... \\ $$

Question Number 134843 Answers: 0 Comments: 1

what is f(x)? such that ((f(x))/x)+f ′(x)ln x=0

$$\mathrm{what}\:\mathrm{is}\:{f}\left({x}\right)? \\ $$$$\mathrm{such}\:\mathrm{that}\:\frac{{f}\left({x}\right)}{{x}}+{f}\:'\left({x}\right)\mathrm{ln}\:{x}=\mathrm{0} \\ $$

Question Number 134841 Answers: 0 Comments: 0

∫_0 ^1 y^2 ln(((y^2 −1)/y^2 ))ln(((y+1)/y))dy From Q134820

$$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{y}^{\mathrm{2}} \mathrm{ln}\left(\frac{\mathrm{y}^{\mathrm{2}} −\mathrm{1}}{\mathrm{y}^{\mathrm{2}} }\right)\mathrm{ln}\left(\frac{\mathrm{y}+\mathrm{1}}{\mathrm{y}}\right)\mathrm{dy} \\ $$$${From}\:{Q}\mathrm{134820} \\ $$

Question Number 134839 Answers: 0 Comments: 1

Solve , S_n = 1+2×2+3×2^2 +4×2^3 +...+n×2^(n−1) .

$$\mathrm{Solve}\:,\:\mathrm{S}_{\mathrm{n}} =\:\mathrm{1}+\mathrm{2}×\mathrm{2}+\mathrm{3}×\mathrm{2}^{\mathrm{2}} +\mathrm{4}×\mathrm{2}^{\mathrm{3}} +...+\mathrm{n}×\mathrm{2}^{\mathrm{n}−\mathrm{1}} . \\ $$

Question Number 134822 Answers: 3 Comments: 0

Question Number 134820 Answers: 1 Comments: 0

Question Number 134817 Answers: 3 Comments: 3

What is the maximum value of abc if a+b+c = 5 and ab+bc+ca = 7?

$$ \\ $$What is the maximum value of abc if a+b+c = 5 and ab+bc+ca = 7?

Question Number 134814 Answers: 1 Comments: 1

Question Number 134812 Answers: 1 Comments: 0

∫(√((1/2)(1+cosh(t))) dt

$$\int\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+{cosh}\left({t}\right)\right.}\:\:{dt} \\ $$

Question Number 134811 Answers: 1 Comments: 0

∫_0 ^( π/2) ((sin (((3x)/2)))/(tan (3x))) dx

$$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{sin}\:\left(\frac{\mathrm{3x}}{\mathrm{2}}\right)}{\mathrm{tan}\:\left(\mathrm{3x}\right)}\:\mathrm{dx} \\ $$

Question Number 134809 Answers: 0 Comments: 0

Show if f ′′(a) exist then f ′′(a)=lim_(h→0) ((f(a+h)+f(a−h)−2f(a))/h^2 )

$${Show}\:{if}\:{f}\:''\left({a}\right)\:{exist}\:{then}\: \\ $$$${f}\:''\left({a}\right)=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{f}\left({a}+{h}\right)+{f}\left({a}−{h}\right)−\mathrm{2}{f}\left({a}\right)}{{h}^{\mathrm{2}} } \\ $$

Question Number 134801 Answers: 1 Comments: 0

Question Number 134798 Answers: 3 Comments: 0

Binomial theorem Given that the coefficient of x^2 in the expansion of (1+ax) (3-2 x) ^5 is 1440, what is the value of the constant a?

$$\mathrm{Binomial}\:\mathrm{theorem} \\ $$Given that the coefficient of x^2 in the expansion of (1+ax) (3-2 x) ^5 is 1440, what is the value of the constant a?

Question Number 134795 Answers: 1 Comments: 0

Question Number 134788 Answers: 1 Comments: 0

Trigonometry If tan^2(α) and tan^2(β) are the roots of the equation 8x^2−26x+15=0, then what is cos(α+β) equal to?

$$\mathrm{Trigonometry} \\ $$If tan^2(α) and tan^2(β) are the roots of the equation 8x^2−26x+15=0, then what is cos(α+β) equal to?

Question Number 134782 Answers: 0 Comments: 0

1,4,16,52,196,... X_n = ???

$$\mathrm{1},\mathrm{4},\mathrm{16},\mathrm{52},\mathrm{196},... \\ $$$$\mathrm{X}_{\mathrm{n}} =\:??? \\ $$

Question Number 134780 Answers: 0 Comments: 0

Question Number 134772 Answers: 3 Comments: 1

What is the equation of a circle that goes through points (0,1), (1,4), and (5,2)?

$$ \\ $$What is the equation of a circle that goes through points (0,1), (1,4), and (5,2)?

Question Number 134770 Answers: 0 Comments: 0

Question Number 134769 Answers: 0 Comments: 5

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