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Question Number 74870 Answers: 1 Comments: 1

solve with explanation lim_(x→0^− ) [(x/(sinx))], where [ ] represents greatest integer

$$\mathrm{solve}\:\mathrm{with}\:\mathrm{explanation} \\ $$$$\mathrm{li}\underset{\mathrm{x}\rightarrow\mathrm{0}^{−} } {\mathrm{m}}\left[\frac{\mathrm{x}}{\mathrm{sinx}}\right],\:\mathrm{where}\:\left[\:\:\right]\:\mathrm{represents}\:\mathrm{greatest}\:\mathrm{integer} \\ $$

Question Number 74863 Answers: 2 Comments: 1

Question Number 76203 Answers: 0 Comments: 7

Question Number 74861 Answers: 1 Comments: 0

Question Number 74860 Answers: 1 Comments: 0

Question Number 74853 Answers: 0 Comments: 2

Is it possible to combine 2cos(90°x)+cos(180°x) into a form of a∙cos(b∙x+c) 2cos((π/2)x)+cos(πx)=^? a∙cos(bx+c)

$$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{combine}\:\mathrm{2}{cos}\left(\mathrm{90}°{x}\right)+{cos}\left(\mathrm{180}°{x}\right) \\ $$$$\mathrm{into}\:\mathrm{a}\:\mathrm{form}\:\mathrm{of}\:\:{a}\centerdot{cos}\left({b}\centerdot{x}+{c}\right) \\ $$$$\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{2}}{x}\right)+{cos}\left(\pi{x}\right)\overset{?} {=}{a}\centerdot{cos}\left({bx}+{c}\right) \\ $$

Question Number 74840 Answers: 0 Comments: 3

Question Number 74825 Answers: 0 Comments: 5

Question Number 74821 Answers: 1 Comments: 0

Question Number 74819 Answers: 1 Comments: 2

Expand Σ ((4n−1)/3)+(2/3)Σ_(k=1) ^(n−1) cos(120k)

$$\mathrm{Expand}\:\Sigma \\ $$$$\frac{\mathrm{4}{n}−\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{3}}\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}{cos}\left(\mathrm{120}{k}\right) \\ $$

Question Number 74817 Answers: 1 Comments: 0

Question Number 74802 Answers: 1 Comments: 4

Question Number 74801 Answers: 2 Comments: 2

{ ((x^2 +y^3 =23)),((x^3 +y^2 =32)) :} solve for x and y .

$$\begin{cases}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{3}} =\mathrm{23}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} =\mathrm{32}}\end{cases}\:\:\:\:\:\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:. \\ $$

Question Number 74800 Answers: 1 Comments: 0

study the existence of f(x)=∫_0 ^∞ ((tcos(tx))/(1+t^2 ))dt

$${study}\:{the}\:{existence}\:{of}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{tcos}\left({tx}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 74799 Answers: 1 Comments: 0

prove that 0≤∫_0 ^∞ ((t^2 e^(−nt) )/(e^t −1))dt ≤(1/n^2 ) for n integr not 0

$${prove}\:{that}\:\mathrm{0}\leqslant\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{t}^{\mathrm{2}} \:{e}^{−{nt}} }{{e}^{{t}} −\mathrm{1}}{dt}\:\leqslant\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\:{for}\:{n}\:{integr}\:{not}\:\mathrm{0} \\ $$

Question Number 74798 Answers: 0 Comments: 0

calculate ∫_0 ^π ln(1−2xcosθ +x^2 )dθ with ∣x∣<1

$${calculate}\:\int_{\mathrm{0}} ^{\pi} {ln}\left(\mathrm{1}−\mathrm{2}{xcos}\theta\:+{x}^{\mathrm{2}} \right){d}\theta\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 74797 Answers: 0 Comments: 0

find nsture of the serie Σ sin(πen!)

$${find}\:{nsture}\:{of}\:{the}\:{serie}\:\Sigma\:{sin}\left(\pi{en}!\right) \\ $$

Question Number 74796 Answers: 0 Comments: 0

let U_n =(−1)^n {arcsin((1/n))−(1/n)}^(1/3) study the convergence of Σ U_n

$${let}\:{U}_{{n}} =\left(−\mathrm{1}\right)^{{n}} \left\{{arcsin}\left(\frac{\mathrm{1}}{{n}}\right)−\frac{\mathrm{1}}{{n}}\right\}^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 74795 Answers: 1 Comments: 1

study the convergence of Σ (1/(nH_n )) with H_n =Σ_(k=1) ^n (1/k)

$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:\frac{\mathrm{1}}{{nH}_{{n}} } \\ $$$${with}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$

Question Number 74794 Answers: 0 Comments: 2

let A = (((1 2)),((−1 1)) ) 1) calculate A^n 2) find e^A and e^(−A) 3) calculate cosA and sinA 4) calculate ch(A) and sh(A)

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{1}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:{cosA}\:{and}\:{sinA} \\ $$$$\left.\mathrm{4}\right)\:{calculate}\:\:{ch}\left({A}\right)\:{and}\:{sh}\left({A}\right) \\ $$

Question Number 74790 Answers: 0 Comments: 0

4x^4 +12x3+25x2t+24x+16 find the square root

$$\mathrm{4}{x}^{\mathrm{4}} +\mathrm{12}{x}\mathrm{3}+\mathrm{25}{x}\mathrm{2}{t}+\mathrm{24}{x}+\mathrm{16}\:{find}\:{the}\:{square}\:{root} \\ $$

Question Number 74786 Answers: 2 Comments: 1

Question Number 74793 Answers: 1 Comments: 1

prove the convergence of ∫_0 ^1 ((ln(1+(√x)))/(√x))dx

$${prove}\:{the}\:{convergence}\:{of}\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}+\sqrt{{x}}\right)}{\sqrt{{x}}}{dx} \\ $$

Question Number 74782 Answers: 1 Comments: 2

Question Number 74776 Answers: 1 Comments: 0

Question Number 74774 Answers: 0 Comments: 0

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