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Question Number 49845 Answers: 1 Comments: 1

y^(xsiny) +x^(ysinx) =1 determine (dy/dx)

$${y}^{{xsiny}} +{x}^{{ysinx}} =\mathrm{1} \\ $$$${determine}\:\frac{{dy}}{{dx}} \\ $$

Question Number 49830 Answers: 3 Comments: 1

Question Number 49829 Answers: 1 Comments: 1

∫(x^2 /(x^4 +1))dx

$$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} +\mathrm{1}}{dx} \\ $$

Question Number 49827 Answers: 1 Comments: 4

The integral ∫_0 ^(1/2) ((ln (1+2x))/(1+4x^2 ))dx = ? a) (π/4)ln2 b)(π/8)ln2 c)(π/(16))ln2 d)(π/(32))ln2

$${The}\:{integral}\:\int_{\mathrm{0}} ^{\frac{\mathrm{1}}{\mathrm{2}}} \frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{2}{x}\right)}{\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} }{dx}\:=\:? \\ $$$$\left.{a}\left.\right)\left.\:\left.\frac{\pi}{\mathrm{4}}{ln}\mathrm{2}\:\:\:\:{b}\right)\frac{\pi}{\mathrm{8}}{ln}\mathrm{2}\:\:\:\:{c}\right)\frac{\pi}{\mathrm{16}}{ln}\mathrm{2}\:\:\:{d}\right)\frac{\pi}{\mathrm{32}}{ln}\mathrm{2} \\ $$

Question Number 49823 Answers: 2 Comments: 0

Complete the square in the expression y^2 +8y+9k and hence find the value of k that makes it a perfect square.

$$\mathrm{Complete}\:\mathrm{the}\:\mathrm{square}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{8y}+\mathrm{9k}\:\mathrm{and}\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{k}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{it}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$

Question Number 49817 Answers: 1 Comments: 1

prove that. ((a^r −1)/r)=1

$$\mathrm{prove}\:\mathrm{that}.\:\frac{\mathrm{a}^{\mathrm{r}} −\mathrm{1}}{\mathrm{r}}=\mathrm{1} \\ $$

Question Number 49816 Answers: 2 Comments: 0

((sin^6 x−cos^6 x)/(sin^2 xcos^2 x)).intregrate

$$\frac{\mathrm{sin}^{\mathrm{6}} \mathrm{x}−\mathrm{cos}^{\mathrm{6}} \mathrm{x}}{\mathrm{sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x}}.\mathrm{intregrate} \\ $$

Question Number 49815 Answers: 0 Comments: 3

sin^6 x−cos^6 x/sin^2 xcos^2 x

$$\mathrm{sin}^{\mathrm{6}} \mathrm{x}−\mathrm{cos}^{\mathrm{6}} \mathrm{x}/\mathrm{sin}^{\mathrm{2}} \mathrm{xcos}^{\mathrm{2}} \mathrm{x} \\ $$

Question Number 49810 Answers: 1 Comments: 1

calculate S_n (x)=[((x+1)/2)] + [((x+2)/4)] +[((x+4)/8)]+...[((x+2^n )/2^(n+1) )]

$${calculate}\: \\ $$$${S}_{{n}} \left({x}\right)=\left[\frac{{x}+\mathrm{1}}{\mathrm{2}}\right]\:+\:\left[\frac{{x}+\mathrm{2}}{\mathrm{4}}\right]\:+\left[\frac{{x}+\mathrm{4}}{\mathrm{8}}\right]+...\left[\frac{{x}+\mathrm{2}^{{n}} }{\mathrm{2}^{{n}+\mathrm{1}} }\right] \\ $$

Question Number 49809 Answers: 2 Comments: 1

solve the system { ((((4(√(1+x^2 )))/x) =((5(√(1+y^2 )))/y)=((6(√(1+z^2 )))/z))),((x+y+z=xyz.)) :} {: (),() }

$${solve}\:{the}\:{system}\:\:\:\begin{cases}{\frac{\mathrm{4}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{{x}}\:=\frac{\mathrm{5}\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }}{{y}}=\frac{\mathrm{6}\sqrt{\mathrm{1}+{z}^{\mathrm{2}} }}{{z}}}\\{{x}+{y}+{z}={xyz}.}\end{cases} \\ $$$$\left.\begin{matrix}{}\\{}\end{matrix}\right\} \\ $$

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

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