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Question Number 102444 Answers: 1 Comments: 0

find the area bounded the curves y^2 = 36+12x and y^2 =16−8x

$${find}\:{the}\:{area}\:{bounded}\:{the} \\ $$$${curves}\:{y}^{\mathrm{2}} =\:\mathrm{36}+\mathrm{12}{x}\:{and}\: \\ $$$${y}^{\mathrm{2}} =\mathrm{16}−\mathrm{8}{x}\: \\ $$

Question Number 102418 Answers: 1 Comments: 0

Question Number 102417 Answers: 3 Comments: 0

calculate ∫_0 ^∞ e^(−x) ln(1+e^x )dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$

Question Number 102416 Answers: 2 Comments: 0

calculate ∫_0 ^1 e^(−x) ln(1+e^x )dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{e}^{−\mathrm{x}} \mathrm{ln}\left(\mathrm{1}+\mathrm{e}^{\mathrm{x}} \right)\mathrm{dx} \\ $$

Question Number 102407 Answers: 0 Comments: 0

Sir MJS & Sir John Santu You both have decided to leave this forum for different reasons. Being agree with your reasons and accepting your right of decision I dare to suggest not to disconnect fully from the forum.Please stay connected although for very short time on daily/weekly basis.This is also necessary because we have no means to contact you. After all this is only a request. You may or may not accept it.

$$\mathrm{Sir}\:\mathrm{MJS}\:\&\:\mathrm{Sir}\:\mathrm{John}\:\mathrm{Santu} \\ $$$${You}\:{both}\:{have}\:{decided}\:{to}\:{leave} \\ $$$${this}\:{forum}\:{for}\:{different}\:{reasons}. \\ $$$${Being}\:{agree}\:{with}\:{your}\:{reasons} \\ $$$${and}\:{accepting}\:{your}\:{right}\:{of}\: \\ $$$${decision}\:{I}\:{dare}\:{to}\:{suggest}\:{not} \\ $$$${to}\:{disconnect}\:{fully}\:{from}\:{the} \\ $$$${forum}.{Please}\:{stay}\:{connected} \\ $$$${although}\:{for}\:{very}\:{short}\:{time}\:{on} \\ $$$${daily}/{weekly}\:{basis}.\mathcal{T}{his}\:{is}\:{also} \\ $$$${necessary}\:{because}\:{we}\:{have}\:{no} \\ $$$${means}\:{to}\:{contact}\:{you}. \\ $$$$\:\:\:\:\mathcal{A}{fter}\:{all}\:{this}\:{is}\:{only}\:{a}\:{request}. \\ $$$${You}\:{may}\:{or}\:{may}\:{not}\:{accept}\:{it}. \\ $$$$ \\ $$

Question Number 102397 Answers: 0 Comments: 0

∫ln(x−(√x)+1)dx

$$\int{ln}\left({x}−\sqrt{{x}}+\mathrm{1}\right){dx} \\ $$

Question Number 102383 Answers: 0 Comments: 2

∫(x/(sin^2 x−3))

$$\int\frac{{x}}{{sin}^{\mathrm{2}} {x}−\mathrm{3}} \\ $$

Question Number 102382 Answers: 1 Comments: 0

x^2 ∙(dy/dx)=x^2 +xy+y^2

$$\mathrm{x}^{\mathrm{2}} \centerdot\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{x}^{\mathrm{2}} +\mathrm{xy}+\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 102381 Answers: 0 Comments: 0

∫((x(√6)sec^2 (x/2))/(1+9tan^4 (x/2)+18tan^2 (x/2)))dx

$$\int\frac{{x}\sqrt{\mathrm{6}}{sec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\mathrm{1}+\mathrm{9}{tan}^{\mathrm{4}} \frac{{x}}{\mathrm{2}}+\mathrm{18}{tan}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{dx} \\ $$

Question Number 102380 Answers: 0 Comments: 0

Question Number 102369 Answers: 3 Comments: 0

find the area bounded inner the curve r = 4−2cos θ and outer the curve r = 6+2cos θ

$${find}\:{the}\:{area}\:{bounded}\:{inner}\:{the}\:{curve} \\ $$$${r}\:=\:\mathrm{4}−\mathrm{2cos}\:\theta\:{and}\:{outer}\:{the}\:{curve}\:{r}\:=\:\mathrm{6}+\mathrm{2cos}\:\theta \\ $$

Question Number 102362 Answers: 0 Comments: 0

please how calculate the development limity of f(x,y)=x^y ,take a( 3,2) at order one and two

$${please}\:{how}\:{calculate}\:{the}\:{development}\:\:{limity}\:{of}\:{f}\left({x},{y}\right)={x}^{{y}} \\ $$$$\:,{take}\:{a}\left(\:\mathrm{3},\mathrm{2}\right)\:{at}\:{order}\:{one}\:{and}\:{two} \\ $$

Question Number 102390 Answers: 2 Comments: 4

asinθ+bcosθ=c acosecθ+bsecθ=c prove that sin2θ=((2ab)/(c^2 −a^2 −b^2 ))

$${asin}\theta+{bcos}\theta={c} \\ $$$${acosec}\theta+{bsec}\theta={c} \\ $$$$ \\ $$$${prove}\:{that}\:\:\:\:{sin}\mathrm{2}\theta=\frac{\mathrm{2}{ab}}{{c}^{\mathrm{2}} −{a}^{\mathrm{2}} −{b}^{\mathrm{2}} } \\ $$

Question Number 102357 Answers: 2 Comments: 0

for A={1,2,3,4,5,6,7},compute the number of: (a) Subsets of A. (b) Nonempty subsets of A. (c) proper subsets of A. (d) Non empty proper subset of A. (e) Subsets of A containing three element. (f) Subsets of A containing 1,2. (g) Proper subsets of A containing 1,2. (h) Subset of A with an even number of element. (i) Subset of A with an odd number of element. (j) Subsets of A with an odd number of elements, including the element 3.

$${for}\:{A}=\left\{\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7}\right\},{compute}\:{the}\:{number}\:{of}: \\ $$$$\left({a}\right)\:{Subsets}\:{of}\:{A}. \\ $$$$\left({b}\right)\:{Nonempty}\:{subsets}\:{of}\:{A}. \\ $$$$\left({c}\right)\:{proper}\:{subsets}\:{of}\:{A}. \\ $$$$\left({d}\right)\:{Non}\:{empty}\:{proper}\:{subset}\:{of}\:{A}. \\ $$$$\left({e}\right)\:{Subsets}\:{of}\:{A}\:{containing}\:{three}\:{element}. \\ $$$$\left({f}\right)\:{Subsets}\:{of}\:{A}\:{containing}\:\mathrm{1},\mathrm{2}. \\ $$$$\left({g}\right)\:{Proper}\:{subsets}\:{of}\:{A}\:{containing}\:\mathrm{1},\mathrm{2}. \\ $$$$\left({h}\right)\:{Subset}\:{of}\:{A}\:{with}\:{an}\:{even}\:{number}\:{of}\:{element}. \\ $$$$\left({i}\right)\:{Subset}\:{of}\:{A}\:{with}\:{an}\:{odd}\:{number}\:{of}\:{element}. \\ $$$$\left({j}\right)\:{Subsets}\:{of}\:{A}\:{with}\:{an}\:{odd}\:{number}\:{of}\:{elements},\:{including}\:{the}\:{element}\:\mathrm{3}. \\ $$

Question Number 102348 Answers: 1 Comments: 0