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Question Number 52590 Answers: 0 Comments: 1

Question Number 52516 Answers: 1 Comments: 0

find the value tanθ+2tan2θ+2^2 tan2^2 θ+2^3 tan2^3 θ+..+2^(n−1) tan2^(n−1) θ

$${find}\:{the}\:{value} \\ $$$${tan}\theta+\mathrm{2}{tan}\mathrm{2}\theta+\mathrm{2}^{\mathrm{2}} {tan}\mathrm{2}^{\mathrm{2}} \theta+\mathrm{2}^{\mathrm{3}} {tan}\mathrm{2}^{\mathrm{3}} \theta+..+\mathrm{2}^{{n}−\mathrm{1}} {tan}\mathrm{2}^{{n}−\mathrm{1}} \theta \\ $$

Question Number 52515 Answers: 2 Comments: 3

1)∫_0 ^∞ ((tan^(−1) (ax)−tan^(−1) (bx))/x)dx 2)∫_0 ^∞ ((e^(−x) sinx)/x)dx

$$\left.\mathrm{1}\right)\int_{\mathrm{0}} ^{\infty} \frac{{tan}^{−\mathrm{1}} \left({ax}\right)−{tan}^{−\mathrm{1}} \left({bx}\right)}{{x}}{dx} \\ $$$$\left.\mathrm{2}\right)\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}} {sinx}}{{x}}{dx} \\ $$

Question Number 52499 Answers: 0 Comments: 0

Let f is a 2^(nd) degree polynomial. (1/(2πi)) ∫_(∣z∣=2) ((z f ′(z))/(f(z))) dz = 0, and (1/(2πi)) ∫_(∣z∣=2) ((z^2 f ′(z))/(f(z))) dz = −2 If f(0) = 2017, find explicit form of f(z)

$$\mathrm{Let}\:{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{degree}\:\mathrm{polynomial}. \\ $$$$\frac{\mathrm{1}}{\mathrm{2}\pi{i}}\:\int_{\mid{z}\mid=\mathrm{2}} \frac{{z}\:{f}\:'\left({z}\right)}{{f}\left({z}\right)}\:{dz}\:=\:\mathrm{0},\:\:\mathrm{and}\:\frac{\mathrm{1}}{\mathrm{2}\pi{i}}\:\int_{\mid{z}\mid=\mathrm{2}} \frac{{z}^{\mathrm{2}} \:{f}\:'\left({z}\right)}{{f}\left({z}\right)}\:{dz}\:=\:−\mathrm{2} \\ $$$$\mathrm{If}\:{f}\left(\mathrm{0}\right)\:=\:\mathrm{2017},\:\mathrm{find}\:\mathrm{explicit}\:\mathrm{form}\:\mathrm{of}\:{f}\left({z}\right) \\ $$

Question Number 52349 Answers: 2 Comments: 3

Determine if the series converges or diverges. (i) Σ_(n = 2) ^∞ (1/(n^2 − 1)) (ii) Σ_(n = 1) ^∞ (1/3^(n − 1) )

$$\mathrm{Determine}\:\mathrm{if}\:\mathrm{the}\:\mathrm{series}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges}. \\ $$$$\:\:\:\left(\mathrm{i}\right)\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{2}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} \:−\:\mathrm{1}} \\ $$$$ \\ $$$$\:\:\:\left(\mathrm{ii}\right)\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{n}\:−\:\mathrm{1}} } \\ $$$$\:\:\: \\ $$

Question Number 52275 Answers: 0 Comments: 0

Question Number 52268 Answers: 0 Comments: 3

Question Number 52240 Answers: 0 Comments: 1

i=what in complex number.

$${i}={what}\:{in}\:{complex}\:{number}. \\ $$

Question Number 52223 Answers: 1 Comments: 2

Question Number 52221 Answers: 0 Comments: 0

a_n =(√(a_(n−1) +a_(n−2) )) a_1 =1 a_2 =3 find explisit to a_n

$${a}_{{n}} =\sqrt{{a}_{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} } \\ $$$${a}_{\mathrm{1}} =\mathrm{1} \\ $$$${a}_{\mathrm{2}} =\mathrm{3} \\ $$$$\mathrm{find}\:\mathrm{explisit}\:\mathrm{to}\:{a}_{{n}} \\ $$

Question Number 52206 Answers: 0 Comments: 1

lim_(x→0) (((1+x)^(1/x) −c)/x)=−(c/2)

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left(\mathrm{1}+{x}\right)^{\mathrm{1}/{x}} −{c}}{{x}}=−\frac{{c}}{\mathrm{2}} \\ $$

Question Number 52214 Answers: 2 Comments: 4

Question Number 52091 Answers: 2 Comments: 1

3^x +4^x =5^x find x BY ISHOLA

$$\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{5}^{{x}} \\ $$$${find}\:{x} \\ $$$${BY}\:{ISHOLA} \\ $$

Question Number 52088 Answers: 0 Comments: 0

determine the value of 5e^(0.5 ) correct to 5 significant fig using d power series of e^x

$${determine}\:{the}\:{value}\:{of}\:\mathrm{5}{e}^{\mathrm{0}.\mathrm{5}\:} \:{correct}\:{to}\:\mathrm{5}\:{significant}\:{fig}\:{using}\:{d}\:{power}\:{series}\:{of}\:{e}^{{x}} \\ $$

Question Number 52079 Answers: 1 Comments: 1

Sum to the n terms of the series whose n^(th ) term is 2^(n−1 ) + 8n^3 −6n^2

$${Sum}\:{to}\:{the}\:{n}\:{terms}\:{of}\:{the}\:{series}\:{whose}\:{n}^{{th}\:} \:{term}\:{is}\:\mathrm{2}^{{n}−\mathrm{1}\:} \:+\:\mathrm{8}{n}^{\mathrm{3}} \:−\mathrm{6}{n}^{\mathrm{2}} \\ $$

Question Number 52075 Answers: 0 Comments: 0

Question Number 52025 Answers: 4 Comments: 8

Question Number 51933 Answers: 2 Comments: 1

If p = cos θ + i sin θ and q = cos φ + i sin φ Show that (((p + q)(pq − 1))/((p − q)(pq + 1))) = ((sin θ + sin φ)/(sin θ − sin φ))

$$\mathrm{If}\:\:\mathrm{p}\:=\:\mathrm{cos}\:\theta\:+\:\mathrm{i}\:\mathrm{sin}\:\theta\:\:\:\:\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\:\:\:\mathrm{q}\:\:=\:\:\mathrm{cos}\:\phi\:+\:\mathrm{i}\:\mathrm{sin}\:\phi \\ $$$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\frac{\left(\mathrm{p}\:+\:\mathrm{q}\right)\left(\mathrm{pq}\:−\:\mathrm{1}\right)}{\left(\mathrm{p}\:−\:\mathrm{q}\right)\left(\mathrm{pq}\:+\:\mathrm{1}\right)}\:\:=\:\:\frac{\mathrm{sin}\:\theta\:+\:\mathrm{sin}\:\phi}{\mathrm{sin}\:\theta\:−\:\mathrm{sin}\:\phi} \\ $$

Question Number 51897 Answers: 1 Comments: 0

If x + (1/x) = 2cosθ , y + (1/y) = 2cosφ , z + (1/z) = 2cosψ Show that xyz + (1/(xyz)) = 2cos(θ + φ + ψ)

$$\mathrm{If}\:\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:\:=\:\:\mathrm{2cos}\theta\:,\:\:\:\:\:\:\mathrm{y}\:+\:\frac{\mathrm{1}}{\mathrm{y}}\:\:=\:\:\mathrm{2cos}\phi\:,\:\:\:\:\:\:\:\:\:\mathrm{z}\:+\:\frac{\mathrm{1}}{\mathrm{z}}\:\:=\:\:\mathrm{2cos}\psi \\ $$$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\:\:\:\:\:\mathrm{xyz}\:+\:\frac{\mathrm{1}}{\mathrm{xyz}}\:\:=\:\:\mathrm{2cos}\left(\theta\:+\:\phi\:+\:\psi\right) \\ $$

Question Number 51887 Answers: 1 Comments: 0

Prove that; tanh(log (√3)) = (1/2)

$$\mathrm{Prove}\:\mathrm{that};\:\:\:\:\mathrm{tanh}\left(\mathrm{log}\:\sqrt{\mathrm{3}}\right)\:\:=\:\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 52140 Answers: 2 Comments: 2

Question Number 51861 Answers: 0 Comments: 1

Question Number 51837 Answers: 1 Comments: 1

Question Number 51721 Answers: 1 Comments: 0

Find the range of value of x given that: ∣x + i∣ ≥ (1/x)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{given}\:\mathrm{that}:\:\:\:\:\:\mid\mathrm{x}\:+\:\mathrm{i}\mid\:\geqslant\:\frac{\mathrm{1}}{\mathrm{x}} \\ $$

Question Number 51673 Answers: 0 Comments: 1

Question Number 51643 Answers: 2 Comments: 0

If ∣z∣ = 1, prove that ((z − 1)/(z^− − 1)) (z ≠ 1) is a pure imaginary

$$\mathrm{If}\:\:\:\mid\mathrm{z}\mid\:=\:\mathrm{1},\:\:\:\:\mathrm{prove}\:\mathrm{that}\:\:\:\:\:\frac{\mathrm{z}\:−\:\mathrm{1}}{\overset{−} {\mathrm{z}}\:−\:\mathrm{1}}\:\:\:\:\:\:\left(\mathrm{z}\:\neq\:\mathrm{1}\right)\:\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{pure}\:\mathrm{imaginary} \\ $$

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