Question and Answers Forum

(1)Determine the following if it is convergent or divergent Σ_(n=1) ^∞ ((sin(n))/n) (2)Σ_(n=1) ^∞ ((sin(n^p ))/n^p ), pεR,find the range of p when it is convergent

$$\left(\mathrm{1}\right){Determine}\:{the}\:{following} \\ $$$${if}\:{it}\:{is}\:{convergent}\:{or}\:{divergent} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}\right)}{{n}} \\ $$$$\left(\mathrm{2}\right)\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}\left({n}^{{p}} \right)}{{n}^{{p}} },\:{p}\epsilon\mathbb{R},{find}\:{the}\:{range}\: \\ $$$${of}\:{p}\:{when}\:{it}\:{is}\:{convergent} \\ $$

Question Number 86111 Answers: 2 Comments: 1

sin (((3π)/2)cos x) = −(1/2)

$$\mathrm{sin}\:\left(\frac{\mathrm{3}\pi}{\mathrm{2}}\mathrm{cos}\:{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 86094 Answers: 1 Comments: 1

2∫(√(x^3 +4)) dx

$$\mathrm{2}\int\sqrt{{x}^{\mathrm{3}} +\mathrm{4}}\:{dx} \\ $$

Question Number 86092 Answers: 1 Comments: 1

∫(1/(√(5−4x−2x^2 )))dx

$$\int\frac{\mathrm{1}}{\sqrt{\mathrm{5}−\mathrm{4}{x}−\mathrm{2}{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 86091 Answers: 1 Comments: 1

∫ ((sin x−cos x)/(√(sin 2x))) dx

$$\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx} \\ $$

Question Number 86088 Answers: 0 Comments: 5

Find the sum of the series below: 1+2+3−4−5−6+7+8+9−10−11−12+13+14+15...−3020

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{below}: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}−\mathrm{4}−\mathrm{5}−\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}−\mathrm{10}−\mathrm{11}−\mathrm{12}+\mathrm{13}+\mathrm{14}+\mathrm{15}...−\mathrm{3020} \\ $$

Question Number 86085 Answers: 1 Comments: 4

If X^2 +Y^2 =10 XY=5 Find (X^2 −Y^2 )

$$\mathrm{If}\:\mathrm{X}^{\mathrm{2}} +\mathrm{Y}^{\mathrm{2}} =\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{XY}=\mathrm{5} \\ $$$$\mathrm{Find}\:\left(\mathrm{X}^{\mathrm{2}} −\mathrm{Y}^{\mathrm{2}} \right) \\ $$

Question Number 86080 Answers: 1 Comments: 1

∫(dx/(√(5−4x−2x^2 )))

$$\int\frac{{dx}}{\sqrt{\mathrm{5}−\mathrm{4}{x}−\mathrm{2}{x}^{\mathrm{2}} }} \\ $$

Question Number 86042 Answers: 3 Comments: 0

solve: ⌊ (√x) ⌋=⌊(x/2)⌋

$${solve}:\:\:\lfloor\:\sqrt{{x}}\:\rfloor=\lfloor\frac{{x}}{\mathrm{2}}\rfloor \\ $$

Question Number 86041 Answers: 2 Comments: 0

1)if sin(θ−x)=k sin(θ+α) find tan(θ) and k then find θ in[0,2π] when k=(1/2) and α=π 2)if x=sin(t) and y=cos(2t) show that (d^2 y/dx^2 )+4=0

$$\left.\mathrm{1}\right){if}\: \\ $$$${sin}\left(\theta−{x}\right)={k}\:{sin}\left(\theta+\alpha\right) \\ $$$${find}\:{tan}\left(\theta\right)\:{and}\:{k} \\ $$$$ \\ $$$${then}\:{find}\:\theta\:{in}\left[\mathrm{0},\mathrm{2}\pi\right]\:\:{when}\:{k}=\frac{\mathrm{1}}{\mathrm{2}}\:{and}\:\alpha=\pi \\ $$$$ \\ $$$$\left.\mathrm{2}\right){if}\:{x}={sin}\left({t}\right)\:\:{and}\:\:{y}={cos}\left(\mathrm{2}{t}\right) \\ $$$${show}\:{that} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{4}=\mathrm{0} \\ $$

Question Number 86040 Answers: 3 Comments: 0

Question Number 86039 Answers: 0 Comments: 1

∫((2x^5 −x^3 −1)/(x^3 −4x))dx

$$\int\frac{\mathrm{2}{x}^{\mathrm{5}} −{x}^{\mathrm{3}} −\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{4}{x}}{dx} \\ $$

Question Number 86120 Answers: 1 Comments: 5

(dy/dx) + ((sin 2y)/x) = x^3 cos^2 y

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\frac{\mathrm{sin}\:\mathrm{2y}}{\mathrm{x}}\:=\:\mathrm{x}^{\mathrm{3}} \:\mathrm{cos}\:^{\mathrm{2}} \:\mathrm{y} \\ $$

Question Number 86034 Answers: 2 Comments: 0

∫(dx/(√(×^2 +4)))

$$\int\frac{{dx}}{\sqrt{×^{\mathrm{2}} +\mathrm{4}}} \\ $$

Question Number 86031 Answers: 1 Comments: 6

lim_(x→0) (((√2)−(√(1+cos x)))/(sin^2 x))=

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2}}−\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}}{\mathrm{sin}\:^{\mathrm{2}} {x}}= \\ $$

Question Number 86030 Answers: 0 Comments: 1

Tbe function f and g are defined by f(x)=2x−3 and g(x)=3x. Find (a) f^(−1) (x) (b) gf(x) (c) gf(2)

$${Tbe}\:{function}\:\boldsymbol{\mathrm{f}}\:{and}\:\boldsymbol{\mathrm{g}}\:{are}\:{defined}\:{by}\:\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{3}\:{and}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\mathrm{3}\boldsymbol{\mathrm{x}}. \\ $$$$\boldsymbol{\mathrm{F}}{ind}\:\left(\boldsymbol{\mathrm{a}}\right)\:\boldsymbol{\mathrm{f}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\:\:\:\:\left(\boldsymbol{\mathrm{b}}\right)\:\boldsymbol{\mathrm{gf}}\left(\boldsymbol{\mathrm{x}}\right)\:\:\:\left(\boldsymbol{\mathrm{c}}\right)\:\boldsymbol{\mathrm{gf}}\left(\mathrm{2}\right) \\ $$

Question Number 86025 Answers: 0 Comments: 1

find the three last digits of 7^(2020) .

$${find}\:{the}\:{three}\:{last}\:{digits}\:{of}\:\:\mathrm{7}^{\mathrm{2020}} . \\ $$

Question Number 86024 Answers: 1 Comments: 1

last three digits of 951413^(314159) =?

$$\mathrm{last}\:\mathrm{three}\:\mathrm{digits}\:\mathrm{of} \\ $$$$\mathrm{951413}^{\mathrm{314159}} =? \\ $$

Question Number 86021 Answers: 0 Comments: 3

E is a vectorial plan in R with a base B=(i^→ ,j^→ ). f is an endomorphism of E defined ∀ u^→ =xi^→ +yj^→ by f(u^→ )=(−7x−12y)i^→ +(4x+7y)j^→ . 1) Determinate f(i^→ ) and f(j^→ ) then write the matrice of f in (i^→ ,j^→ )base.

Pg 1255 Pg 1256 Pg 1257 Pg 1258 Pg 1259 Pg 1260 Pg 1261 Pg 1262 Pg 1263 Pg 1264

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