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Question Number 44356 Answers: 0 Comments: 0

Question Number 44355 Answers: 0 Comments: 0

Question Number 44351 Answers: 1 Comments: 1

If is an even function defined on the interval (−5,5) then a value of x satisfying the equation f(x)=f(((x+1)/(x+2))) is a)((−1+(√5))/2) b)((−3+(√5))/2) c)((−1−(√5))/2) d)((−3−(√5))/2_ )

$${If}\:{is}\:{an}\:{even}\:{function}\:{defined}\:{on} \\ $$$${the}\:{interval}\:\left(−\mathrm{5},\mathrm{5}\right)\:{then}\:{a}\:{value} \\ $$$${of}\:{x}\:{satisfying}\:{the}\:{equation} \\ $$$${f}\left({x}\right)={f}\left(\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\right)\:{is} \\ $$$$\left.{a}\left.\right)\left.\frac{−\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\:{b}\right)\frac{−\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}}\:{c}\right)\frac{−\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}\: \\ $$$$\left.{d}\right)\frac{−\mathrm{3}−\sqrt{\mathrm{5}}}{\mathrm{2}_{} } \\ $$

Question Number 44350 Answers: 0 Comments: 3

If f(x+y)=f(x).f(y) for real x,y and f(0)≠0.Let F(x)=((f(x))/(1+(f(x))^2 )) then F(x) is a)even b)odd c)neither even nor odd

$${If}\:{f}\left({x}+{y}\right)={f}\left({x}\right).{f}\left({y}\right)\:{for}\:{real}\:{x},{y} \\ $$$${and}\:{f}\left(\mathrm{0}\right)\neq\mathrm{0}.{Let}\:{F}\left({x}\right)=\frac{{f}\left({x}\right)}{\mathrm{1}+\left({f}\left({x}\right)\right)^{\mathrm{2}} } \\ $$$${then}\:{F}\left({x}\right)\:{is} \\ $$$$\left.{a}\left.\right)\left.{even}\:{b}\right){odd}\:{c}\right){neither}\:{even}\:{nor}\:{odd} \\ $$

Question Number 44346 Answers: 0 Comments: 0

Question Number 44336 Answers: 0 Comments: 0

Question Number 44334 Answers: 1 Comments: 0

Question Number 44333 Answers: 0 Comments: 2

Can positive integers a, b, c be found such that a^3 + b^3 = c^(3 ) ?

$$\mathrm{Can}\:\mathrm{positive}\:\mathrm{integers}\:\:\mathrm{a},\:\mathrm{b},\:\mathrm{c}\:\:\mathrm{be}\:\mathrm{found}\:\mathrm{such}\:\mathrm{that}\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:=\:\mathrm{c}^{\mathrm{3}\:\:\:} ? \\ $$

Question Number 44325 Answers: 0 Comments: 1

Question Number 44324 Answers: 2 Comments: 0

5 2 a + 3 5 ___ the addition on the left is in base 6.find a. 1001

$$\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{2}\:{a} \\ $$$$\:\:\:\:+\:\:\:\:\mathrm{3}\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\_\_\_\:\:\:\:\:{the}\:{addition}\:{on}\:{the}\:{left}\:{is}\:{in}\:{base}\:\mathrm{6}.{find}\:{a}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1001} \\ $$

Question Number 44319 Answers: 1 Comments: 2

find lim_(x→0^+ ) ∫_x ^(2x) ((√(1+t^2 ))/t)dt .

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}{{t}}{dt}\:. \\ $$

Question Number 44318 Answers: 1 Comments: 2

let f(x)=∫_x ^(+∞) (e^(−t) /t)dt 1)calculate f^′ (x) 2)find a equivalent of f(x) when x→+∞.

$${let}\:{f}\left({x}\right)=\int_{{x}} ^{+\infty} \:\frac{{e}^{−{t}} }{{t}}{dt} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{a}\:{equivalent}\:{of}\:{f}\left({x}\right)\:{when} \\ $$$${x}\rightarrow+\infty. \\ $$

Question Number 44315 Answers: 1 Comments: 0

If the sum of the coefficients in the expansion of (1+2x)^n is 6561, then the greatest coefficient in the expansion is

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{coefficients}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+\mathrm{2}{x}\right)^{{n}} \:\mathrm{is}\:\mathrm{6561},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{is} \\ $$

Question Number 44309 Answers: 0 Comments: 2

find the value of I =∫_(−∞) ^(+∞) ((cos(αt))/((x^2 +x +1)^2 ))dx α from R. 2)calculate ∫_(−∞) ^(+∞) (dx/((x^2 +x +1)^2 ))

$${find}\:{the}\:{value}\:{of}\: \\ $$$${I}\:=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{cos}\left(\alpha{t}\right)}{\left({x}^{\mathrm{2}} \:+{x}\:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\alpha\:{from}\:{R}. \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+{x}\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 44308 Answers: 1 Comments: 2

let I = ∫_0 ^∞ cos^4 t e^(−2t) dt and J=∫_0 ^∞ sin^4 t e^(−2t) dt 1) calculate I +J and I−J 2)find the values of I and J.

$${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:{cos}^{\mathrm{4}} {t}\:{e}^{−\mathrm{2}{t}} {dt}\:{and}\:{J}=\int_{\mathrm{0}} ^{\infty} \:{sin}^{\mathrm{4}} {t}\:{e}^{−\mathrm{2}{t}} {dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:+{J}\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{values}\:{of}\:{I}\:{and}\:{J}. \\ $$

Question Number 44307 Answers: 0 Comments: 0

find ∫_0 ^(π/2) cosxln(cosx)dx

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {cosxln}\left({cosx}\right){dx} \\ $$

Question Number 44306 Answers: 0 Comments: 2

find ∫ (dt/((t+1)(√t) +t(√(t+1)))) 2) calculate ∫_1 ^3 (dt/((t+1)(√t)+t(√(t+1))))

$${find}\:\int\:\:\frac{{dt}}{\left({t}+\mathrm{1}\right)\sqrt{{t}}\:+{t}\sqrt{{t}+\mathrm{1}}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\frac{{dt}}{\left({t}+\mathrm{1}\right)\sqrt{{t}}+{t}\sqrt{{t}+\mathrm{1}}} \\ $$

Question Number 44305 Answers: 0 Comments: 1

let f(a) =∫_0 ^∞ ln(1+(a^2 /x^2 ))dx 1) find a explicit form of f(x) 2)find ∫_0 ^∞ ln(1+(1/x^2 ))dx 3)calculate ∫_0 ^∞ ln(1+(2/x^2 ))dx

$${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\mathrm{1}+\frac{{a}^{\mathrm{2}} }{{x}^{\mathrm{2}} }\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){dx} \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:{ln}\left(\mathrm{1}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} }\right){dx} \\ $$

Question Number 44304 Answers: 1 Comments: 2

find f(a)=∫_0 ^(π/4) (dx/(1+acos^2 x)) a from R.

$${find}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\mathrm{1}+{acos}^{\mathrm{2}} {x}} \\ $$$${a}\:{from}\:{R}. \\ $$

Question Number 44302 Answers: 2 Comments: 1

calculate ∫_0 ^∞ (dx/((x+1)(x+2)(x+3)))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)\left({x}+\mathrm{3}\right)} \\ $$

Question Number 44301 Answers: 0 Comments: 1

Prove that 1 + (1/2^2 ) + (1/3^2 ) + (1/4^2 ) + ... = (π^2 /6)

$${Prove}\:\:{that} \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{2}} }\:+\:...\:\:=\:\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 44298 Answers: 1 Comments: 2

α_1 and α_2 are the temperature coefficients of the two resistors R_1 and R_2 at any temperature T_0 0°C.Find the equivalent resistance if both R_1 and R_(2 ) are connected in series combination.Assume that α_1 and α_2 remain same with change in temperature.

$$\alpha_{\mathrm{1}} \:{and}\:\alpha_{\mathrm{2}} \:{are}\:{the}\:{temperature} \\ $$$${coefficients}\:{of}\:{the}\:{two}\:{resistors} \\ $$$${R}_{\mathrm{1}} \:{and}\:{R}_{\mathrm{2}} \:{at}\:{any}\:{temperature}\:{T}_{\mathrm{0}} \\ $$$$\mathrm{0}°{C}.{Find}\:{the}\:{equivalent}\:{resistance} \\ $$$${if}\:{both}\:{R}_{\mathrm{1}} \:{and}\:{R}_{\mathrm{2}\:} \:{are}\:{connected}\:{in} \\ $$$${series}\:{combination}.{Assume}\:{that} \\ $$$$\alpha_{\mathrm{1}} \:{and}\:\alpha_{\mathrm{2}} \:{remain}\:{same}\:{with}\:{change} \\ $$$${in}\:{temperature}. \\ $$

Question Number 44317 Answers: 1 Comments: 0

let u_n =∫_0 ^∞ ((t−[t])/(t(t+n)))dt find a equivalent of u_n when n→+∞

$${let}\:{u}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}−\left[{t}\right]}{{t}\left({t}+{n}\right)}{dt} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:{when}\:{n}\rightarrow+\infty \\ $$

Question Number 44291 Answers: 1 Comments: 5

withiout using calculator find approximate for (√(9.01))

$${withiout}\:{using}\:{calculator}\:{find}\:{approximate}\:{for} \\ $$$$\sqrt{\mathrm{9}.\mathrm{01}} \\ $$

Question Number 44267 Answers: 1 Comments: 0

If xε ((1/(√2)) , 1) ,differentiate cos^(−1) (2x(√(1−x^2 ))).

$${If}\:{x}\epsilon\:\left(\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:,\:\mathrm{1}\right)\:,{differentiate}\:\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{2}{x}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right). \\ $$

Question Number 44264 Answers: 1 Comments: 1

∫(1/((x^2 +2x+5)^2 ))dx

$$\int\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$

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