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Question Number 35336 Answers: 2 Comments: 1

(√(2x^2 ))+7x+5(√2)=0

$$\sqrt{\mathrm{2}{x}^{\mathrm{2}} }+\mathrm{7}{x}+\mathrm{5}\sqrt{\mathrm{2}}=\mathrm{0} \\ $$

Question Number 35325 Answers: 1 Comments: 0

Sketch the region enclosed by the curves of y=1/x and y=1/x^2 and find the area of the region. plzz help me

$${Sketch}\:{the}\:{region}\:{enclosed}\:{by}\:{the} \\ $$$${curves}\:{of}\:{y}=\mathrm{1}/{x}\:{and}\:{y}=\mathrm{1}/{x}^{\mathrm{2}} \:{and} \\ $$$${find}\:{the}\:{area}\:{of}\:{the}\:{region}. \\ $$$${plzz}\:{help}\:{me} \\ $$

Question Number 35419 Answers: 1 Comments: 0

Given that f(x)= x^3 −x^2 +ax+b and g(x)= 2x^3 −9x^2 −3ax + b have a common factor (x−1) where a and b are constands . Find the values of a and b hence find other factors of f(x)

$${Given}\:{that}\: \\ $$$${f}\left({x}\right)=\:{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{ax}+{b}\:{and}\: \\ $$$${g}\left({x}\right)=\:\mathrm{2}{x}^{\mathrm{3}} −\mathrm{9}{x}^{\mathrm{2}} −\mathrm{3}{ax}\:+\:{b}\:{have}\:{a} \\ $$$${common}\:{factor}\:\left({x}−\mathrm{1}\right)\:{where}\:{a}\:{and} \\ $$$${b}\:{are}\:{constands}\:.\:{Find}\:{the}\:{values} \\ $$$${of}\:{a}\:{and}\:{b}\:{hence}\:{find}\:{other}\:{factors} \\ $$$${of}\:{f}\left({x}\right) \\ $$

Question Number 35313 Answers: 0 Comments: 0

Question Number 35304 Answers: 2 Comments: 4

Q1. a) solve for x 9^x +5(3^x )=6 b)write down the first 4 terms in the binomial expansion of (1−3x)^7 c)the sum S_n of the first n^(th) terms is given by S_(n ) = 3(1−((2/3))^n ) find d) the common ratio e) the sum to infinity of the progression

$$\left.\:{Q}\mathrm{1}.\:\:\:{a}\right)\:{solve}\:{for}\:{x}\:\:\mathrm{9}^{{x}} +\mathrm{5}\left(\mathrm{3}^{{x}} \right)=\mathrm{6} \\ $$$$\left.{b}\right){write}\:{down}\:{the}\:{first}\:\:\mathrm{4}\:{terms} \\ $$$${in}\:{the}\:{binomial}\:{expansion}\:{of}\:\left(\mathrm{1}−\mathrm{3}{x}\right)^{\mathrm{7}} \\ $$$$\left.{c}\right){the}\:{sum}\:{S}_{{n}} \:{of}\:{the}\:{first}\:{n}^{{th}} {terms} \\ $$$${is}\:{given}\:{by}\:{S}_{{n}\:} =\:\mathrm{3}\left(\mathrm{1}−\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{{n}} \right)\:{find} \\ $$$$\left.{d}\right)\:{the}\:{common}\:{ratio} \\ $$$$\left.{e}\right)\:{the}\:{sum}\:{to}\:{infinity}\:{of}\:{the}\:{progression} \\ $$

Question Number 35300 Answers: 0 Comments: 0

Question Number 35297 Answers: 0 Comments: 1

sokve x^3 +6y^3 =4z^3 x y z integers

$${sokve}\:{x}^{\mathrm{3}} +\mathrm{6}{y}^{\mathrm{3}} =\mathrm{4}{z}^{\mathrm{3}} \:{x}\:{y}\:{z}\:{integers} \\ $$

Question Number 35294 Answers: 1 Comments: 1

Question Number 35291 Answers: 1 Comments: 1

solve in Z x^3 +6y^3 =4z^3

$${solve}\:\:{in}\:{Z}\:\:{x}^{\mathrm{3}} +\mathrm{6}{y}^{\mathrm{3}} =\mathrm{4}{z}^{\mathrm{3}} \\ $$

Question Number 35290 Answers: 0 Comments: 1

∫((x+1)/x^3 )dx

$$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} }{dx} \\ $$

Question Number 35319 Answers: 2 Comments: 0

Question Number 35267 Answers: 1 Comments: 0

Question Number 35265 Answers: 0 Comments: 0

4−4×4+4=

$$\mathrm{4}−\mathrm{4}×\mathrm{4}+\mathrm{4}= \\ $$

Question Number 35279 Answers: 0 Comments: 3

Question Number 35256 Answers: 1 Comments: 1

Factorize :x^5 −y^5

$$\mathrm{Factorize}\::\mathrm{x}^{\mathrm{5}} −\mathrm{y}^{\mathrm{5}} \\ $$

Question Number 35248 Answers: 0 Comments: 1

Question Number 35246 Answers: 1 Comments: 1

if x^p + y^q =(x + y)^(p+q) prove that (dy/dx)=(y/x)

$${if}\:{x}^{{p}} \:+\:{y}^{{q}} \:=\left({x}\:+\:{y}\right)^{{p}+{q}} \: \\ $$$${prove}\:{that}\:\frac{{dy}}{{dx}}=\frac{{y}}{{x}} \\ $$

Question Number 35245 Answers: 0 Comments: 7

express ((7x+4)/(x^3 +x^2 + 9x +9)) in partial fraction

$${express}\:\frac{\mathrm{7}{x}+\mathrm{4}}{{x}^{\mathrm{3}} \:+{x}^{\mathrm{2}} +\:\mathrm{9}{x}\:+\mathrm{9}}\:{in}\:{partial} \\ $$$${fraction} \\ $$

Question Number 35244 Answers: 0 Comments: 1

if y=((sin^(−1) x)/(1−x^2 )) show that (1−x^2 )(dy/dx) −xy=1

$${if}\:\:{y}=\frac{{sin}^{−\mathrm{1}} {x}}{\mathrm{1}−{x}^{\mathrm{2}} }\:\:{show}\:{that}\: \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right)\frac{{dy}}{{dx}}\:−{xy}=\mathrm{1} \\ $$

Question Number 35242 Answers: 1 Comments: 1

find ∫_0 ^π ((xdx)/(1+sinx))

$${find}\:\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{xdx}}{\mathrm{1}+{sinx}} \\ $$

Question Number 35241 Answers: 2 Comments: 6

calculate ∫_0 ^π ((x dx)/(3 +cosx)) .

$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\:\:\frac{{x}\:{dx}}{\mathrm{3}\:+{cosx}}\:\:. \\ $$

Question Number 35238 Answers: 0 Comments: 1

study the convergence of ∫_1 ^(+∞) ((e^(−3x) −e^(−2x) )/x^2 )dx

$${study}\:{the}\:{convergence}\:{of} \\ $$$$\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{e}^{−\mathrm{3}{x}} \:−{e}^{−\mathrm{2}{x}} }{{x}^{\mathrm{2}} }{dx}\: \\ $$

Question Number 35237 Answers: 0 Comments: 1

study the convergence of ∫_0 ^∞ ((e^(−x) −e^(−x^2 ) )/x)dx .

$${study}\:{the}\:{convergence}\:{of} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{x}} \:−{e}^{−{x}^{\mathrm{2}} } }{{x}}{dx}\:. \\ $$

Question Number 35236 Answers: 0 Comments: 0

letf(x)=arctan(1+ix) with ∣x∣<1 developp f at integr serie.

$${letf}\left({x}\right)={arctan}\left(\mathrm{1}+{ix}\right)\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$${developp}\:{f}\:\:{at}\:{integr}\:{serie}. \\ $$

Question Number 35235 Answers: 0 Comments: 2

let f(x)= e^(−2x) arctanx 1) calculate f^((n)) (x) 2) find f^((n)) (0) 3) developp f at integr serie

$${let}\:{f}\left({x}\right)=\:{e}^{−\mathrm{2}{x}} \:{arctanx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 35234 Answers: 0 Comments: 1

let f(x) =e^(−x^n ) with n fromN developp f at integr serie .

$${let}\:{f}\left({x}\right)\:={e}^{−{x}^{{n}} } \:\:\:\:\:{with}\:{n}\:{fromN} \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

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