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Question Number 63164 Answers: 0 Comments: 0

let S_n =Σ_(k=1) ^n (((−1)^k )/k) and H_n =Σ_(k=1) ^n (1/k) calculate S_n interms of H_n 2)find lim_(n→+∞) S_n

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\:\:\:\:\:{and}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$$${calculate}\:{S}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$

Question Number 63162 Answers: 1 Comments: 3

Find the set of values of x which satisfy the inequalities (2/(x−1))≤(1/x) and x^2 −∣3x∣+2<0

$${Find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{x}\:{which}\:{satisfy}\:{the}\:{inequalities}\: \\ $$$$\frac{\mathrm{2}}{{x}−\mathrm{1}}\leqslant\frac{\mathrm{1}}{{x}}\:\:{and}\:\:{x}^{\mathrm{2}} −\mid\mathrm{3}{x}\mid+\mathrm{2}<\mathrm{0} \\ $$

Question Number 63154 Answers: 0 Comments: 5

Given that α and β are the roots oc the equation ax^2 +bx+c=0 . Show that λμb^2 = ac(λ + μ)^2 , where (α/β)= (λ/μ).

$${Given}\:{that}\:\alpha\:{and}\:\beta\:{are}\:{the}\:{roots}\:{oc}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$$.\:{Show}\:{that}\:\:\:\lambda\mu{b}^{\mathrm{2}} =\:{ac}\left(\lambda\:+\:\mu\right)^{\mathrm{2}} ,\:{where}\:\frac{\alpha}{\beta}=\:\frac{\lambda}{\mu}. \\ $$

Question Number 63152 Answers: 0 Comments: 0

The Variables x and y satisfy the differential equation (d^2 y/dx^2 )−x(dy/dx) + y = x^2 use the approximations ((d^2 y/dx^2 ))_n ≈ ((y_(n+1) −2y_n +y_(n−1) )/h^(2 ) ) and ((dy/dx))≈((y_(n+1) −y_(n−1) )/(2h )) to show that (2−hx_n )y_(n+1) ≈2x_n ^2 + 398y_n −(200 + 10x_n )y_(n−1) given that y=1 and x=0 and that y_(−1) =y_1 show that y_1 =0.995 Evaluate y when x=0.3, giving your answercorrect to 3 decimal places

$${The}\:{Variables}\:{x}\:{and}\:{y}\:{satisfy}\:{the}\:{differential}\:{equation}\: \\ $$$$\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−{x}\frac{{dy}}{{dx}}\:+\:{y}\:=\:{x}^{\mathrm{2}} \:\:{use}\:{the}\:{approximations} \\ $$$$\:\:\:\left(\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\right)_{{n}} \approx\:\frac{{y}_{{n}+\mathrm{1}} −\mathrm{2}{y}_{{n}} +{y}_{{n}−\mathrm{1}} }{{h}^{\mathrm{2}\:} }\:{and}\:\:\left(\frac{{dy}}{{dx}}\right)\approx\frac{{y}_{{n}+\mathrm{1}} −{y}_{{n}−\mathrm{1}} }{\mathrm{2}{h}\:}\:{to}\:{show}\:{that} \\ $$$$\:\:\left(\mathrm{2}−{hx}_{{n}} \right){y}_{{n}+\mathrm{1}} \approx\mathrm{2}{x}_{{n}} ^{\mathrm{2}} \:+\:\mathrm{398}{y}_{{n}} −\left(\mathrm{200}\:+\:\mathrm{10}{x}_{{n}} \right){y}_{{n}−\mathrm{1}} \\ $$$${given}\:{that}\:{y}=\mathrm{1}\:{and}\:{x}=\mathrm{0}\:{and}\:{that}\:{y}_{−\mathrm{1}} ={y}_{\mathrm{1}} \:{show}\:{that}\:{y}_{\mathrm{1}} =\mathrm{0}.\mathrm{995} \\ $$$${Evaluate}\:{y}\:{when}\:{x}=\mathrm{0}.\mathrm{3},\:{giving}\:{your}\:{answercorrect}\:{to}\:\mathrm{3}\:{decimal}\:{places} \\ $$

Question Number 63143 Answers: 0 Comments: 0

Question Number 63139 Answers: 0 Comments: 3

Σ_(n = 1) ^m ((log n)/n^(3/2) )

$$\underset{\mathrm{n}\:=\:\mathrm{1}} {\overset{\mathrm{m}} {\sum}}\:\frac{\mathrm{log}\:\mathrm{n}}{\mathrm{n}^{\mathrm{3}/\mathrm{2}} } \\ $$

Question Number 63137 Answers: 1 Comments: 0

please who can prove the half−life in radioactivity formula of t_(1/2) = ((ln2)/λ) where λ is distergration rate. Involving ln(N_0 /N_t )= λt

$${please}\:{who}\:{can}\:{prove}\:{the}\:{half}−{life}\:{in}\:{radioactivity}\:{formula} \\ $$$${of}\:\:{t}_{\frac{\mathrm{1}}{\mathrm{2}}} =\:\frac{{ln}\mathrm{2}}{\lambda}\:\:{where}\:\lambda\:{is}\:{distergration}\:{rate}.\:{Involving}\: \\ $$$${ln}\frac{{N}_{\mathrm{0}} }{{N}_{{t}} }=\:\lambda{t} \\ $$

Question Number 63128 Answers: 0 Comments: 7

Examine the following function for extreme value f(x, y) = x^4 + y^4 − 2x^3 + 4xy − 2y^2

$$\mathrm{Examine}\:\mathrm{the}\:\mathrm{following}\:\mathrm{function}\:\mathrm{for}\:\mathrm{extreme}\:\mathrm{value} \\ $$$$\:\:\:\:\mathrm{f}\left(\mathrm{x},\:\mathrm{y}\right)\:\:=\:\:\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:−\:\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{4xy}\:−\:\mathrm{2y}^{\mathrm{2}} \\ $$

Question Number 63124 Answers: 1 Comments: 5

A solenoid is 40cm long,has a cross sectional area of 8.0cm^2 and is wound with 309 turns of wire that carries a current of 1.2A.The relative permeability of the iron core is 600. Compute the B for the interior point and the flux through the solenoid.

$${A}\:{solenoid}\:{is}\:\mathrm{40}{cm}\:{long},{has}\:{a}\:{cross} \\ $$$${sectional}\:{area}\:{of}\:\mathrm{8}.\mathrm{0}{cm}^{\mathrm{2}} \:{and}\:{is}\:{wound} \\ $$$${with}\:\mathrm{309}\:{turns}\:{of}\:{wire}\:{that}\:{carries}\:{a} \\ $$$${current}\:{of}\:\mathrm{1}.\mathrm{2}{A}.{The}\:{relative} \\ $$$${permeability}\:{of}\:{the}\:{iron}\:{core}\:{is}\:\mathrm{600}. \\ $$$${Compute}\:{the}\:\boldsymbol{{B}}\:{for}\:{the}\:{interior}\:{point} \\ $$$${and}\:{the}\:{flux}\:{through}\:{the}\:{solenoid}. \\ $$

Question Number 63121 Answers: 0 Comments: 3

x^(1/2) ∙ x^(1/4) ∙ x^(1/8) ∙ x^(1/16) ... to ∞ is equal to

$${x}^{\mathrm{1}/\mathrm{2}} \:\centerdot\:{x}^{\mathrm{1}/\mathrm{4}} \:\centerdot\:{x}^{\mathrm{1}/\mathrm{8}} \:\centerdot\:{x}^{\mathrm{1}/\mathrm{16}} \:...\:\mathrm{to}\:\infty\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 63120 Answers: 0 Comments: 0

x^(1/2) ∙ x^(1/4) ∙ x^(1/8) ∙ x^(1/16) ... to ∞ is equal to

Question Number 63117 Answers: 1 Comments: 1

∫((cos x)/(2+3sin x+sin^2 x))dx

$$\int\frac{\mathrm{cos}\:{x}}{\mathrm{2}+\mathrm{3sin}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 63116 Answers: 1 Comments: 1

∫((1+×)/(√(1+×^2 )))dx

$$\int\frac{\mathrm{1}+×}{\sqrt{\mathrm{1}+×^{\mathrm{2}} }}{dx} \\ $$

Question Number 63108 Answers: 2 Comments: 1

Question Number 63103 Answers: 1 Comments: 2

Question Number 63101 Answers: 3 Comments: 1

calculate S =(1/(1×2)) +(1/(3×4)) +(1/(5×6)) +.....

$${calculate}\:\:{S}\:=\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}\:+\frac{\mathrm{1}}{\mathrm{5}×\mathrm{6}}\:+..... \\ $$

Question Number 63095 Answers: 1 Comments: 0

Question Number 63090 Answers: 0 Comments: 0

s=(√(a^2 +(a^2 −d)^2 ))+(√((b−a)^2 +(b^2 −a^2 )^2 )) +(√(b^2 +(c−b^2 )^2 ))+c−d p= a(a^2 −d)+(a+b)(b^2 −a^2 ) +b(c−b^2 ) Find a,b,c, or d in terms of s if p is maximum. Assume a,b,c,d ≥0 .

$${s}=\sqrt{{a}^{\mathrm{2}} +\left({a}^{\mathrm{2}} −{d}\right)^{\mathrm{2}} }+\sqrt{\left({b}−{a}\right)^{\mathrm{2}} +\left({b}^{\mathrm{2}} −{a}^{\mathrm{2}} \right)^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+\sqrt{{b}^{\mathrm{2}} +\left({c}−{b}^{\mathrm{2}} \right)^{\mathrm{2}} }+{c}−{d} \\ $$$$\:{p}=\:{a}\left({a}^{\mathrm{2}} −{d}\right)+\left({a}+{b}\right)\left({b}^{\mathrm{2}} −{a}^{\mathrm{2}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:+{b}\left({c}−{b}^{\mathrm{2}} \right) \\ $$$${Find}\:{a},{b},{c},\:{or}\:{d}\:\:{in}\:{terms}\:{of}\:{s} \\ $$$${if}\:\:{p}\:{is}\:{maximum}.\: \\ $$$${Assume}\:\:\:\:{a},{b},{c},{d}\:\geqslant\mathrm{0}\:. \\ $$

Question Number 63089 Answers: 0 Comments: 3

find the value of ∫_0 ^(π/2) (dx/(1+(tanx)^(√2) )) .

$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}+\left({tanx}\right)^{\sqrt{\mathrm{2}}} }\:. \\ $$

Question Number 63084 Answers: 0 Comments: 1

let f(z) =((cos(3z))/z^2 ) calculate Res(f,0) .

$${let}\:{f}\left({z}\right)\:=\frac{{cos}\left(\mathrm{3}{z}\right)}{{z}^{\mathrm{2}} } \\ $$$${calculate}\:{Res}\left({f},\mathrm{0}\right)\:. \\ $$

Question Number 63080 Answers: 0 Comments: 0

∫((√((sinx)/x^3 ))/x^3 )dx

$$\:\int\frac{\sqrt{\frac{{sinx}}{{x}^{\mathrm{3}} }}}{{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 63079 Answers: 0 Comments: 1

let f(z) =((sin(2z))/z^n ) with n integr natural calculate Res(f,0)