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AllQuestion and Answers: Page 1185

Question Number 97591 Answers: 1 Comments: 0

∫(x^4 /(x^3 −2x^2 −7x+4))dx

$$\int\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{4}}{dx} \\ $$

Question Number 97590 Answers: 1 Comments: 0

find the integration ∫(√(sin(x)))dx

$$\mathrm{find}\:\mathrm{the}\:\mathrm{integration} \\ $$$$\int\sqrt{{sin}\left({x}\right)}{dx} \\ $$

Question Number 97577 Answers: 2 Comments: 1

lim_(x→1) ((4x lnx)/(x−1)) =??

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{4}{x}\:\mathrm{ln}{x}}{{x}−\mathrm{1}}\:=?? \\ $$

Question Number 97576 Answers: 2 Comments: 0

Show that RE[(1/(1−z))]=(1/2) where z = cos θ + i sinθ

$$\:\mathrm{Show}\:\mathrm{that}\:{RE}\left[\frac{\mathrm{1}}{\mathrm{1}−{z}}\right]=\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{where}\:{z}\:=\:\mathrm{cos}\:\theta\:+\:{i}\:\mathrm{sin}\theta \\ $$$$ \\ $$

Question Number 97569 Answers: 1 Comments: 0

∫_0 ^(π/4) (√(tan(x)))(√(1−tan(x))) dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \sqrt{{tan}\left({x}\right)}\sqrt{\mathrm{1}−{tan}\left({x}\right)}\:{dx} \\ $$

Question Number 97564 Answers: 1 Comments: 0

Question Number 97563 Answers: 1 Comments: 0

∫_0 ^(+∞) e^(−x) cos(x^2 )dx. Discuss the convergence of this generalised intergral. Please help

$$\int_{\mathrm{0}} ^{+\infty} \mathrm{e}^{−\mathrm{x}} \mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\mathrm{dx}. \\ $$$$\mathrm{Discuss}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{of}\:\mathrm{this}\: \\ $$$$\mathrm{generalised}\:\mathrm{intergral}. \\ $$$$\mathrm{Please}\:\mathrm{help} \\ $$

Question Number 97557 Answers: 1 Comments: 0

Question Number 97555 Answers: 0 Comments: 8

Question Number 97554 Answers: 1 Comments: 5

Find all the triples of positive integers (x;y;z) so that ((x−y(√(2020)))/(y−z(√(2020)))) is a rational number and x^2 +y^2 +z^2 be a prime number.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{triples}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{integers}\:\left(\mathrm{x};\mathrm{y};\mathrm{z}\right) \\ $$$$\mathrm{so}\:\mathrm{that}\:\frac{\mathrm{x}−\mathrm{y}\sqrt{\mathrm{2020}}}{\mathrm{y}−\mathrm{z}\sqrt{\mathrm{2020}}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{rational}\:\mathrm{number} \\ $$$$\mathrm{and}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \mathrm{be}\:\mathrm{a}\:\mathrm{prime}\:\mathrm{number}. \\ $$

Question Number 97552 Answers: 2 Comments: 0

∫_0 ^1 (√(x/(1−x))) ln((x/(1−x))) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\frac{{x}}{\mathrm{1}−{x}}}\:\mathrm{ln}\left(\frac{{x}}{\mathrm{1}−{x}}\right)\:{dx}\:? \\ $$

Question Number 97550 Answers: 0 Comments: 0

Question Number 97546 Answers: 0 Comments: 2

Question Number 97541 Answers: 1 Comments: 2

Determinate lim_(x→1/2) ((sin(2x−1))/(2x−1)) lim_(x→+∞ ) ((cosx)/(1+x^(2 ) ))

$${Determinate} \\ $$$$\underset{{x}\rightarrow\mathrm{1}/\mathrm{2}} {{lim}}\:\frac{{sin}\left(\mathrm{2}{x}−\mathrm{1}\right)}{\mathrm{2}{x}−\mathrm{1}} \\ $$$$\underset{{x}\rightarrow+\infty\:} {{lim}}\:\frac{{cosx}}{\mathrm{1}+{x}^{\mathrm{2}\:} } \\ $$

Question Number 97539 Answers: 2 Comments: 0

x^2 −3y^2 +2xy (dy/dx) = 0

$${x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{2}{xy}\:\frac{{dy}}{{dx}}\:=\:\mathrm{0} \\ $$

Question Number 97537 Answers: 1 Comments: 0

∫_0 ^1 ((−(√(1−x^2 )))/((yx^3 +x^2 −yx−1)))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{\left({yx}^{\mathrm{3}} +{x}^{\mathrm{2}} −{yx}−\mathrm{1}\right)}{dx} \\ $$

Question Number 97531 Answers: 1 Comments: 0

5050((∫_0 ^1 (1−x^(50) )^(100) dx)/(∫_0 ^1 (1−x^(50) )^(101) dx))=

$$\mathrm{5050}\frac{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{50}} \right)^{\mathrm{100}} {dx}}{\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{50}} \right)^{\mathrm{101}} {dx}}= \\ $$

Question Number 97527 Answers: 0 Comments: 0

∫((xdx)/(x!))=?

$$\int\frac{\mathrm{xdx}}{\mathrm{x}!}=? \\ $$

Question Number 97526 Answers: 1 Comments: 1

∫(dx/(1+sin x))=?

$$\int\frac{\mathrm{dx}}{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}=? \\ $$

Question Number 97512 Answers: 0 Comments: 2

The value of k for which the quadratic equation (1−2k)x^2 −6kx−1=0 and kx^2 −x+1=0 have atleast one roots in common are ___

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the} \\ $$$$\mathrm{quadratic}\:\mathrm{equation}\:\left(\mathrm{1}−\mathrm{2k}\right)\mathrm{x}^{\mathrm{2}} −\mathrm{6kx}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{kx}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}=\mathrm{0}\:\mathrm{have}\:\mathrm{atleast} \\ $$$$\mathrm{one}\:\mathrm{roots}\:\mathrm{in}\:\mathrm{common}\:\mathrm{are}\:\_\_\_ \\ $$

Question Number 97506 Answers: 0 Comments: 0

please prove it cos x= J_0 (x) + 2Σ_(x−1) (−1)^x J_(2n) (x)

$${please}\:{prove}\:{it} \\ $$$$ \\ $$$$\mathrm{cos}\:{x}=\:{J}_{\mathrm{0}} \left({x}\right)\:+\:\mathrm{2}\sum_{{x}−\mathrm{1}} \left(−\mathrm{1}\right)^{{x}} {J}_{\mathrm{2}{n}} \left({x}\right) \\ $$

Question Number 97501 Answers: 0 Comments: 2

The natural number n for which the expression y = 5log^2 _3 (n) − log _3 (n^(12) )+9 , has the minimum value is ___

$$\mathrm{The}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{n}\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\mathrm{the}\:\mathrm{expression}\:\mathrm{y}\:=\:\mathrm{5log}^{\mathrm{2}} \:_{\mathrm{3}} \left(\mathrm{n}\right)\:− \\ $$$$\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{n}^{\mathrm{12}} \right)+\mathrm{9}\:,\:\mathrm{has}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 97505 Answers: 0 Comments: 0

Question Number 97497 Answers: 2 Comments: 0

Question Number 97496 Answers: 1 Comments: 0

if f(((2x+5)/(x−3)))=3x+5 find f(x) please solve it

$${if}\:\:\:\:\:\:{f}\left(\frac{\mathrm{2}{x}+\mathrm{5}}{{x}−\mathrm{3}}\right)=\mathrm{3}{x}+\mathrm{5}\:\:\:{find}\:\:\:{f}\left({x}\right) \\ $$$$ \\ $$$${please}\:{solve}\:{it} \\ $$

Question Number 97494 Answers: 1 Comments: 0

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