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Question Number 40236 Answers: 1 Comments: 0

if a b c are in H.P then prove that (a/(b+c)),(b/(c+a)),(c/(a+b)) arw also in H.P.

$${if}\:{a}\:{b}\:{c}\:{are}\:{in}\:{H}.{P}\:{then}\:{prove}\:{that}\:\frac{{a}}{{b}+{c}},\frac{{b}}{{c}+{a}},\frac{{c}}{{a}+{b}}\:\:{arw} \\ $$$${also}\:{in}\:{H}.{P}. \\ $$

Question Number 40231 Answers: 1 Comments: 0

Question Number 40222 Answers: 1 Comments: 0

please help Kate was given 602.00 dollas for shopping. She spent (1/4) on chocolate and later (2/3) on goods. How much money was left?

$$\mathrm{please}\:\mathrm{help} \\ $$$$\mathrm{Kate}\:\mathrm{was}\:\mathrm{given}\:\mathrm{602}.\mathrm{00}\:\mathrm{dollas}\:\mathrm{for}\: \\ $$$$\mathrm{shopping}.\:\mathrm{She}\:\mathrm{spent}\:\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{on}\:\mathrm{chocolate} \\ $$$$\mathrm{and}\:\mathrm{later}\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{on}\:\mathrm{goods}.\:\mathrm{How}\:\mathrm{much} \\ $$$$\mathrm{money}\:\mathrm{was}\:\mathrm{left}? \\ $$

Question Number 40218 Answers: 2 Comments: 0

find the nth term and the sum to n termof the following seried (i) 4+6+9+13+18+... (ii) 11+23+59+167+...

$${find}\:{the}\:{nth}\:{term}\:{and}\:{the}\:{sum}\:{to}\:{n}\:\:{termof}\:{the}\:{following}\:{seried} \\ $$$$\left({i}\right)\:\mathrm{4}+\mathrm{6}+\mathrm{9}+\mathrm{13}+\mathrm{18}+... \\ $$$$\left({ii}\right)\:\mathrm{11}+\mathrm{23}+\mathrm{59}+\mathrm{167}+... \\ $$

Question Number 40216 Answers: 1 Comments: 0

Question Number 40213 Answers: 0 Comments: 0

Question Number 40212 Answers: 2 Comments: 1

Solve 4x^2 −8x−3=0

$${Solve}\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{8}{x}−\mathrm{3}=\mathrm{0} \\ $$

Question Number 40188 Answers: 0 Comments: 0

can any one plss answer question ; 40057

$${can}\:{any}\:{one}\:{plss}\:{answer} \\ $$$${question}\:;\:\mathrm{40057} \\ $$

Question Number 40186 Answers: 0 Comments: 0

Question Number 40185 Answers: 0 Comments: 0

Question Number 40176 Answers: 0 Comments: 0

Question Number 40173 Answers: 1 Comments: 1

Question Number 40945 Answers: 0 Comments: 0

Two parallel plate conductors 1m from each other carry an electric current of 2A each.Find the magnetic force per metre on each wire.

$${Two}\:{parallel}\:{plate}\:{conductors}\:\mathrm{1}{m} \\ $$$${from}\:{each}\:{other}\:{carry}\:{an}\:{electric} \\ $$$${current}\:{of}\:\mathrm{2}{A}\:{each}.{Find}\:{the}\:{magnetic} \\ $$$${force}\:{per}\:{metre}\:{on}\:{each}\:{wire}. \\ $$

Question Number 40170 Answers: 1 Comments: 3

Question Number 40161 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ ((sin((1/x^2 )))/(ln(1+(√x))))dx

$${study}\:{the}\:{convergence}\:{of}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{sin}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)}{{ln}\left(\mathrm{1}+\sqrt{{x}}\right)}{dx} \\ $$

Question Number 40160 Answers: 0 Comments: 1

study the convergence of ∫_0 ^1 ((1−e^(−t) )/(t(√t))) dt

$${study}\:{the}\:{convergence}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{\mathrm{1}−{e}^{−{t}} }{{t}\sqrt{{t}}}\:{dt} \\ $$

Question Number 40159 Answers: 0 Comments: 1

let I_n = ∫_0 ^∞ (dx/((1+x^3 )^n )) find a relation etween I_n and I_(n+1) 2) calculate I_(1 ) and I_2

$${let}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)^{{n}} } \\ $$$${find}\:{a}\:{relation}\:{etween}\:{I}_{{n}} \:{and}\:{I}_{{n}+\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{\mathrm{1}\:} \:{and}\:{I}_{\mathrm{2}} \\ $$

Question Number 40158 Answers: 0 Comments: 3

let A_n = ∫_0 ^1 ((x^(2n+1) ln(x))/(x^2 −1))dx 1) justify the existence of A_n 2)calculate A_(n+1) −A_n 3) prove that x∈]0,1[ ⇒0<((xln(x))/(x^2 −1))<(1/2) 4) find lim_(n→+∞) A_n

$${let}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} \:{ln}\left({x}\right)}{{x}^{\mathrm{2}} \:−\mathrm{1}}{dx} \\ $$$$\left.\mathrm{1}\right)\:{justify}\:{the}\:{existence}\:{of}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{A}_{{n}+\mathrm{1}} \:−{A}_{{n}} \\ $$$$\left.\mathrm{3}\left.\right)\:{prove}\:{that}\:\:{x}\in\right]\mathrm{0},\mathrm{1}\left[\:\Rightarrow\mathrm{0}<\frac{{xln}\left({x}\right)}{{x}^{\mathrm{2}} \:−\mathrm{1}}<\frac{\mathrm{1}}{\mathrm{2}}\:\:\right. \\ $$$$\left.\mathrm{4}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} {A}_{{n}} \\ $$

Question Number 40157 Answers: 1 Comments: 1

find the value of ∫_(−∞) ^(+∞) (dt/((t^2 −2t +2)^(3/2) ))

$${find}\:{the}\:{value}\:{of}\:\:\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{dt}}{\left({t}^{\mathrm{2}} \:−\mathrm{2}{t}\:+\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$

Question Number 40156 Answers: 1 Comments: 1

find ∫_e^2 ^(+∞) (dt/(tln(t)ln(ln(t)))

$${find}\:\:\:\int_{{e}^{\mathrm{2}} } ^{+\infty} \:\:\:\:\frac{{dt}}{{tln}\left({t}\right){ln}\left({ln}\left({t}\right)\right.} \\ $$

Question Number 40155 Answers: 1 Comments: 1

caoculate ∫_0 ^∞ ((t dt)/((1+t^4 )^2 ))

$${caoculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{t}\:{dt}}{\left(\mathrm{1}+{t}^{\mathrm{4}} \right)^{\mathrm{2}} } \\ $$

Question Number 40154 Answers: 1 Comments: 1

find the value of ∫_0 ^1 ((ln(t))/((1+t)^2 ))dt

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{ln}\left({t}\right)}{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} }{dt} \\ $$

Question Number 40153 Answers: 1 Comments: 1

calculate ∫_1 ^2 ((t−2)/(√(t^2 −1)))dt

$${calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{2}} \:\:\:\frac{{t}−\mathrm{2}}{\sqrt{{t}^{\mathrm{2}} \:−\mathrm{1}}}{dt} \\ $$

Question Number 40152 Answers: 1 Comments: 1

let f(x) = ∫_(−1) ^x (e^t /(√(1−e^t )))dt with x<0 1) calculate f(x) 2) find ∫_(−1) ^0 (e^t /(√(1−e^t )))dt

$${let}\:\:{f}\left({x}\right)\:=\:\:\int_{−\mathrm{1}} ^{{x}} \:\:\:\:\frac{{e}^{{t}} }{\sqrt{\mathrm{1}−{e}^{{t}} }}{dt}\:\:\:{with}\:{x}<\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\int_{−\mathrm{1}} ^{\mathrm{0}} \:\:\frac{{e}^{{t}} }{\sqrt{\mathrm{1}−{e}^{{t}} }}{dt} \\ $$

Question Number 40151 Answers: 1 Comments: 1

let F(x) = ∫_0 ^(π/2) cos(xsint)dt 1) prove that ∀u ∈R 1−(u^2 /2) ≤cosu≤1−(u^2 /2) +(u^4 /(24)) 2) prove that (π/2)(1−(x^2 /4))≤F(x)≤ (π/2)(1−(x^2 /4) +(x^4 /(64)))

$${let}\:{F}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}\left({xsint}\right){dt} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:\:\forall{u}\:\in{R}\:\:\mathrm{1}−\frac{{u}^{\mathrm{2}} }{\mathrm{2}}\:\leqslant{cosu}\leqslant\mathrm{1}−\frac{{u}^{\mathrm{2}} }{\mathrm{2}}\:+\frac{{u}^{\mathrm{4}} }{\mathrm{24}} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{4}}\right)\leqslant{F}\left({x}\right)\leqslant\:\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\frac{{x}^{\mathrm{2}} }{\mathrm{4}}\:+\frac{{x}^{\mathrm{4}} }{\mathrm{64}}\right) \\ $$

Question Number 40150 Answers: 0 Comments: 1

let f_n (x) =(1/((1+x^n )^(1+(1/n)) )) ddfined on [0,1] 1) prove that f_n →^(cs) f (n→+∞) 2) calculate I_n = ∫_0 ^1 f_n (x)dx

$${let}\:{f}_{{n}} \left({x}\right)\:=\frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{{n}} \right)^{\mathrm{1}+\frac{\mathrm{1}}{{n}}} }\:\:\:{ddfined}\:{on}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}_{{n}} \rightarrow^{{cs}} \:{f}\:\left({n}\rightarrow+\infty\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}_{{n}} \left({x}\right){dx} \\ $$$$ \\ $$

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