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AllQuestion and Answers: Page 1663

Question Number 41783 Answers: 1 Comments: 0

Question Number 41606 Answers: 2 Comments: 0

4x^4 +16x^3 +24x^2 −9x−1=0 using any method. find real value of x that satisfy the polynomial

Question Number 41586 Answers: 2 Comments: 1

f(x)=(√(−3+(√((x+1)/(x−1))))) ∫f(x)=? ∫f^(−1) (x)=?

$${f}\left({x}\right)=\sqrt{−\mathrm{3}+\sqrt{\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}}} \\ $$$$\int{f}\left({x}\right)=? \\ $$$$\int{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 41579 Answers: 1 Comments: 1

If u_(10) = ∫_( 0) ^(π/2) x^(10) sin x dx, then the value of u_(10) +90 u_8 is

$$\mathrm{If}\:\:{u}_{\mathrm{10}} =\:\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}^{\mathrm{10}} \:\mathrm{sin}\:{x}\:{dx},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$${u}_{\mathrm{10}} +\mathrm{90}\:{u}_{\mathrm{8}} \:\:\mathrm{is} \\ $$

Question Number 41578 Answers: 0 Comments: 0

If u_(10) = ∫_( 0) ^(π/2) x^(10) sin x dx, then the value of u_(10) +90 u_8 is

Question Number 41561 Answers: 2 Comments: 3

∫ (dx/(3sin(x) + 4cos(x)))

$$\int\:\frac{\mathrm{dx}}{\mathrm{3sin}\left(\mathrm{x}\right)\:+\:\mathrm{4cos}\left(\mathrm{x}\right)} \\ $$

Question Number 41577 Answers: 0 Comments: 0

If u_(10) = ∫_( 0) ^(π/2) x^(10) sin x dx, then the value of u_(10) +90 u_8 is

Question Number 41555 Answers: 5 Comments: 0

Question Number 41536 Answers: 3 Comments: 0

if y=(√(((1+sinx)/(1−sinx)) )) show that (dy/dx)=(1/(1−sinx))

$$\boldsymbol{\mathrm{if}}\:\boldsymbol{{y}}=\sqrt{\frac{\mathrm{1}+\boldsymbol{\mathrm{sin}{x}}}{\mathrm{1}−\boldsymbol{\mathrm{sin}{x}}}\:}\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{{dy}}}{\boldsymbol{{dx}}}=\frac{\mathrm{1}}{\mathrm{1}−\boldsymbol{\mathrm{sin}{x}}} \\ $$

Question Number 41534 Answers: 1 Comments: 0

Three chidren are playing the game of claping hands,the first child claping hands in every after 1sec,the second child clap hands in every after 10sec and the third child claps in every after 5sec. for how long do all three children will clap their hands together at the same time?

Question Number 41530 Answers: 1 Comments: 0

Question Number 41522 Answers: 2 Comments: 2

Find the cube root of 26 − 15(√3)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{root}\:\mathrm{of}\:\:\:\mathrm{26}\:−\:\mathrm{15}\sqrt{\mathrm{3}} \\ $$

Question Number 41521 Answers: 0 Comments: 0

let A(−1,1) and B(0,3) find image of the line (AB) by 1) translation t_u^→ with u^→ (1−2i) 2) rotation R(w,(π/3)) with w(1+i)

$${let}\:{A}\left(−\mathrm{1},\mathrm{1}\right)\:{and}\:{B}\left(\mathrm{0},\mathrm{3}\right)\:\:\:{find}\:\:\:{image}\:{of}\:{the}\:{line}\:\left({AB}\right)\:{by} \\ $$$$\left.\mathrm{1}\right)\:{translation}\:{t}_{\overset{\rightarrow} {{u}}} \:\:\:\:{with}\:\overset{\rightarrow} {{u}}\left(\mathrm{1}−\mathrm{2}{i}\right) \\ $$$$\left.\mathrm{2}\right)\:{rotation}\:{R}\left({w},\frac{\pi}{\mathrm{3}}\right)\:\:{with}\:{w}\left(\mathrm{1}+{i}\right) \\ $$

Question Number 41520 Answers: 3 Comments: 0

let Z = cos(((2π)/7)) +isin(((2π)/7)) and A= Z+Z^2 +Z^4 B=Z^3 +Z^5 +Z^6 1) prove that A^− =B 2) prove that A+B =−1 and A.B =2 3) find A and B.

$${let}\:{Z}\:=\:{cos}\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\:+{isin}\left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)\:{and}\:\:{A}=\:{Z}+{Z}^{\mathrm{2}} \:+{Z}^{\mathrm{4}} \\ $$$${B}={Z}^{\mathrm{3}} \:+{Z}^{\mathrm{5}} \:+{Z}^{\mathrm{6}} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\overset{−} {{A}}={B} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:{A}+{B}\:=−\mathrm{1}\:{and}\:{A}.{B}\:=\mathrm{2} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\:{A}\:{and}\:{B}. \\ $$$$ \\ $$

Question Number 41519 Answers: 2 Comments: 0

let z=(√(2−(√3))) −i(√(2+(√3))) calculate ∣z^n ∣ and arg(z^n )

$${let}\:{z}=\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\:\:−{i}\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}} \\ $$$${calculate}\:\mid{z}^{{n}} \mid\:\:{and}\:{arg}\left({z}^{{n}} \right) \\ $$

Question Number 41518 Answers: 3 Comments: 0

calculate A_n = ∫_0 ^1 (1−t^2 )^n dt with n integr natural

$${calculate}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{t}^{\mathrm{2}} \right)^{{n}} {dt}\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 41517 Answers: 1 Comments: 1

let S_n = 1 +(1/((^3 (√2)))) + (1/((^3 (√3)))) + ....+(1/((^3 (√n)))) calculate lim _(n→+∞) S_n

$${let}\:\:{S}_{{n}} =\:\mathrm{1}\:+\frac{\mathrm{1}}{\left(^{\mathrm{3}} \sqrt{\mathrm{2}}\right)}\:+\:\frac{\mathrm{1}}{\left(^{\mathrm{3}} \sqrt{\mathrm{3}}\right)}\:+\:....+\frac{\mathrm{1}}{\left(^{\mathrm{3}} \sqrt{{n}}\right)} \\ $$$${calculate}\:{lim}\:_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$

Question Number 41516 Answers: 1 Comments: 1

calculate ∫_0 ^1 ((ln(1+x))/((1+x)^4 )) dx

$${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{ln}\left(\mathrm{1}+{x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{4}} }\:{dx} \\ $$

Question Number 41515 Answers: 1 Comments: 3

let f_n (x) =((sin(2(n+1)x))/(sinx)) if x∈]0,(π/2)] and f_n (0)=2(n+1) let u_n = ∫_0 ^(π/2) f_n (x)dx 1) prove that ∀n fromN u_(n+1) −u_n =2(((−1)^(n+1) )/(2n+3)) 2)find lim_(n→+∞) u_n

$$\left.{l}\left.{et}\:\:{f}_{{n}} \left({x}\right)\:=\frac{{sin}\left(\mathrm{2}\left({n}+\mathrm{1}\right){x}\right)}{{sinx}}\:{if}\:\:{x}\in\right]\mathrm{0},\frac{\pi}{\mathrm{2}}\right]\:{and}\:{f}_{{n}} \left(\mathrm{0}\right)=\mathrm{2}\left({n}+\mathrm{1}\right)\:\:{let} \\ $$$${u}_{{n}} =\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{f}_{{n}} \left({x}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\forall{n}\:{fromN}\:\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} =\mathrm{2}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{\mathrm{2}{n}+\mathrm{3}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{u}_{{n}} \\ $$

Question Number 41514 Answers: 1 Comments: 0

find ∫ cos(lnx)dx

$${find}\:\:\:\int\:\:{cos}\left({lnx}\right){dx}\: \\ $$

Question Number 41513 Answers: 2 Comments: 0

let A_n = ∫_0 ^∞ e^(−nx^2 ) cos(x^2 ) dx and B_n =∫_0 ^∞ e^(−nx^2 ) sin(x^2 )dx (n∈ N^★ ) 1) calculate A_n and B_n 2) find lim_(n→+∞) (A_n /B_n )

$${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}^{\mathrm{2}} } {cos}\left({x}^{\mathrm{2}} \right)\:{dx}\:\:{and}\:\:{B}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{nx}^{\mathrm{2}} } {sin}\left({x}^{\mathrm{2}} \right){dx}\:\:\:\:\left({n}\in\:{N}^{\bigstar} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{A}_{{n}} \:{and}\:\:{B}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{A}_{{n}} }{{B}_{{n}} } \\ $$

Question Number 41512 Answers: 0 Comments: 0

let u_n =(1/1^3 ) +(1/2^3 ) +....+(1/n^3 ) 1)prove that (9/8) −(1/(2(n+1)^2 )) ≤ u_n ≤ (3/2) −(1/(2n^2 )) 2) prove that ∀ n∈N^★ 1≤u_n ≤ (3/2) 3) prove that (u_n )is convegente .

$${let}\:\:{u}_{{n}} =\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }\:+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }\:+....+\frac{\mathrm{1}}{{n}^{\mathrm{3}} } \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:\:\:\frac{\mathrm{9}}{\mathrm{8}}\:−\frac{\mathrm{1}}{\mathrm{2}\left({n}+\mathrm{1}\right)^{\mathrm{2}} }\:\leqslant\:{u}_{{n}} \leqslant\:\frac{\mathrm{3}}{\mathrm{2}}\:−\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\forall\:{n}\in{N}^{\bigstar} \:\:\:\mathrm{1}\leqslant{u}_{{n}} \leqslant\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left.\mathrm{3}\right)\:{prove}\:{that}\:\left({u}_{{n}} \right){is}\:{convegente}\:. \\ $$

Question Number 41508 Answers: 0 Comments: 0

A facial surgery is estimated to cost N25millon in 10 years time. A 50 years old woman that is expecting to go on retirement at 55years is planning to generate funds for the surgery at her retirement. ow much should she set aside for the surgery if the interest rate is 14.75% at the time of retirement? what is the present value of the cost of surgery?(as at the time the woman is 50years given the interest rate at that time is 11.5%)

Question Number 41495 Answers: 2 Comments: 3

The equation π^x =−2x^2 +6x−9 has

$$\mathrm{The}\:\mathrm{equation}\:\pi^{{x}} =−\mathrm{2}{x}^{\mathrm{2}} +\mathrm{6}{x}−\mathrm{9}\:\mathrm{has} \\ $$

Question Number 41488 Answers: 2 Comments: 0

Question Number 41487 Answers: 3 Comments: 4

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