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Question Number 49806 Answers: 0 Comments: 1

let f(x) =∫_0 ^(π/4) ln(1−x^2 cosθ)dθ with ∣x∣<1 1) find a explicit form of f(x) 2) calculate ∫_0 ^(π/4) ln(1−(1/4)cosθ)dθ .

$${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} {cos}\theta\right){d}\theta\:\:\:{with}\:\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{4}}{cos}\theta\right){d}\theta\:. \\ $$

Question Number 49804 Answers: 0 Comments: 1

let f(x) =(e^(−x) /(x+1)) 1) calculate f^((n)) (o) and f^((n)) (1) 2) developp f at integr serie .

$${let}\:{f}\left({x}\right)\:=\frac{{e}^{−{x}} }{{x}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}^{\left({n}\right)} \left({o}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$

Question Number 49803 Answers: 0 Comments: 0

find lim_(x→0^+ ) (((sinx)^x −1)/(x^(sinx) −1))

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:\:\:\frac{\left({sinx}\right)^{{x}} \:−\mathrm{1}}{{x}^{{sinx}} \:−\mathrm{1}} \\ $$

Question Number 49802 Answers: 1 Comments: 0

find lim_(x→e) ((e^x −e^e )/(x^e −e^e ))

$${find}\:{lim}_{{x}\rightarrow{e}} \:\:\:\frac{{e}^{{x}} \:−{e}^{{e}} }{{x}^{{e}} \:−{e}^{{e}} } \\ $$

Question Number 49800 Answers: 1 Comments: 0

find lim_(x→0) (((√(1+x+x^2 ))−(√(1+2x+x^3 )))/x^2 )

$${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{\sqrt{\mathrm{1}+{x}+{x}^{\mathrm{2}} }−\sqrt{\mathrm{1}+\mathrm{2}{x}+{x}^{\mathrm{3}} }}{{x}^{\mathrm{2}} } \\ $$

Question Number 49798 Answers: 0 Comments: 0

help me sir Plzzz

$$\mathrm{help}\:\mathrm{me}\:\mathrm{sir}\:\mathrm{Plzzz} \\ $$

Question Number 49796 Answers: 0 Comments: 0

Question Number 49790 Answers: 0 Comments: 1

thank you very much Sir

$$\mathrm{thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{Sir} \\ $$

Question Number 49786 Answers: 0 Comments: 1

Sir l couldn′t solve these questions pls help me

$$\mathrm{Sir}\:\mathrm{l}\:\mathrm{couldn}'\mathrm{t}\:\mathrm{solve}\:\mathrm{these}\:\mathrm{questions} \\ $$$$\mathrm{pls}\:\mathrm{help}\:\mathrm{me} \\ $$

Question Number 49785 Answers: 1 Comments: 0

Question Number 49776 Answers: 0 Comments: 0

could you help me sir

$$\mathrm{could}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{sir} \\ $$

Question Number 49774 Answers: 1 Comments: 0

Question Number 49765 Answers: 2 Comments: 1

Solve for x in R : 2 × sin(3x+4) + (√( 3 )) = 0

$$\mathrm{Solve}\:\mathrm{for}\:{x}\:\mathrm{in}\:\mathbb{R}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{2}\:×\:\mathrm{sin}\left(\mathrm{3}{x}+\mathrm{4}\right)\:+\:\sqrt{\:\mathrm{3}\:}\:=\:\mathrm{0} \\ $$

Question Number 49764 Answers: 0 Comments: 0

sir help me pls

$$\mathrm{sir}\:\mathrm{help}\:\mathrm{me}\:\mathrm{pls} \\ $$$$ \\ $$

Question Number 49763 Answers: 0 Comments: 0

Question Number 49767 Answers: 1 Comments: 0

Question Number 49768 Answers: 0 Comments: 1

help me sir plz

$$\mathrm{help}\:\mathrm{me}\:\mathrm{sir}\:\mathrm{plz} \\ $$$$ \\ $$

Question Number 49761 Answers: 1 Comments: 0

Calculate : ∫(( sin^2 x cos^2 x)/((sin^3 x+cos^3 x)^2 )) dx

$${Calculate}\:: \\ $$$$\:\int\frac{\:\:\mathrm{sin}^{\mathrm{2}} {x}\:\mathrm{cos}^{\mathrm{2}} {x}}{\left(\mathrm{sin}^{\mathrm{3}} {x}+\mathrm{cos}^{\mathrm{3}} {x}\right)^{\mathrm{2}} }\:{dx} \\ $$

Question Number 49760 Answers: 0 Comments: 3

Question Number 49755 Answers: 1 Comments: 0

Solve simultaneously for s in terms of a and b. h^2 +(b−k)^2 = s^2 .....(i) (h^2 /a^2 )+(k^2 /b^2 ) = 1 .....(ii) (h−(s/2))^2 +(k+b(√(1−(s^2 /(4a^2 )))) )= s^2 ..(iii).

$${Solve}\:{simultaneously}\:{for}\:\boldsymbol{{s}}\:{in}\:{terms} \\ $$$${of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}. \\ $$$${h}^{\mathrm{2}} +\left({b}−{k}\right)^{\mathrm{2}} =\:{s}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:.....\left({i}\right) \\ $$$$\frac{{h}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{k}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:=\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....\left({ii}\right) \\ $$$$\left({h}−\frac{{s}}{\mathrm{2}}\right)^{\mathrm{2}} +\left({k}+{b}\sqrt{\mathrm{1}−\frac{{s}^{\mathrm{2}} }{\mathrm{4}{a}^{\mathrm{2}} }}\:\right)=\:{s}^{\mathrm{2}} \:\:\:..\left({iii}\right). \\ $$

Question Number 49751 Answers: 1 Comments: 1

The value of tan^(−1) (1/2) + tan^(−1) (1/3) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}\:+\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{3}}\:\:\mathrm{is} \\ $$

Question Number 49746 Answers: 1 Comments: 0

∫((sin^8 x−cos^8 x)/(1−2sin^2 x.cos^2 x)) = ? a) ((−1)/2)sin 2x b)(1/2)sin 2x c)None.

$$\int\frac{\mathrm{sin}^{\mathrm{8}} {x}−\mathrm{cos}^{\mathrm{8}} {x}}{\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} {x}.\mathrm{cos}^{\mathrm{2}} {x}}\:=\:? \\ $$$$\left.{a}\left.\right)\left.\:\frac{−\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}\:\:\:{b}\right)\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sin}\:\mathrm{2}{x}\:\:\:{c}\right){None}. \\ $$

Question Number 49740 Answers: 1 Comments: 1

Question Number 49737 Answers: 1 Comments: 1

Question Number 49736 Answers: 1 Comments: 1

there is two small and one grater circles that [two]are tangent to [one]and all three circles are inscribed in an ellipse with: [(a/b)=2(√2)]and tangent to it at two points such that center of circles are on major axe of ellipse. find: ((radi of great circle)/(radi of small circle)) .

Question Number 49731 Answers: 1 Comments: 0

one vertex of a equilateral triangle lies on one vertex of a square and two anothers lie on opposite sides of square such that triangle have the maximum area. find: 1.ratio of: ((square side)/(triangle side)) 2.angle between square side and triangle side.[need additional data?]

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