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Question Number 83395 Answers: 0 Comments: 0

Let R be a relation such that R = {3,6,12,24} prove that R is a strict order relation.

$$\mathrm{Let}\:\mathrm{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{relation}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{R}\:=\:\left\{\mathrm{3},\mathrm{6},\mathrm{12},\mathrm{24}\right\} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{R}\:\mathrm{is}\:\mathrm{a}\:\mathrm{strict}\:\mathrm{order} \\ $$$$\mathrm{relation}.\: \\ $$

Question Number 83385 Answers: 2 Comments: 1

∫((1+ae^(−(a+1)x) +(a+1)e^(−ax) )/x^2 ) dx, a∈z^+

$$\int\frac{\mathrm{1}+{ae}^{−\left({a}+\mathrm{1}\right){x}} +\left({a}+\mathrm{1}\right){e}^{−{ax}} }{{x}^{\mathrm{2}} }\:{dx},\:\:{a}\in{z}^{+} \\ $$

Question Number 83383 Answers: 1 Comments: 0

find ∫_0 ^2 ∫_0 ^(√(4−x^2 )) ∫_0 ^(2−z) zdxdydz pleas help me sir

$${find}\:\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} \int_{\mathrm{0}} ^{\mathrm{2}−{z}} {zdxdydz} \\ $$$${pleas}\:{help}\:{me}\:{sir} \\ $$

Question Number 83381 Answers: 0 Comments: 0

Given that the function f(x) = x^3 is differentiable in the interval (−2,2) us the mean value theorem to find the value of x for which the tangent to the curve is parrallel to the chord through the points (−2,8) and (2,8).

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:\mathrm{is}\: \\ $$$$\mathrm{differentiable}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\left(−\mathrm{2},\mathrm{2}\right)\:\mathrm{us}\:\mathrm{the}\:\mathrm{mean} \\ $$$$\mathrm{value}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\: \\ $$$$\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{is}\:\mathrm{parrallel}\:\mathrm{to}\:\mathrm{the}\:\mathrm{chord}\: \\ $$$$\mathrm{through}\:\mathrm{the}\:\mathrm{points}\:\left(−\mathrm{2},\mathrm{8}\right)\:\mathrm{and}\:\left(\mathrm{2},\mathrm{8}\right). \\ $$

Question Number 83378 Answers: 0 Comments: 2

x+y+z=1 x^2 +y^2 +z^2 =2 x^3 +y^3 +z^3 =3 find x^4 +y^4 +z^4 =?

$${x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =\mathrm{3} \\ $$$${find} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} =? \\ $$

Question Number 83373 Answers: 0 Comments: 4

Question Number 83372 Answers: 0 Comments: 1

Question Number 83370 Answers: 0 Comments: 3

Question Number 83369 Answers: 1 Comments: 2

Question Number 83367 Answers: 0 Comments: 1

∫_(−∞) ^∞ ((sin^7 (x))/x^7 )dx

$$\int_{−\infty} ^{\infty} \frac{{sin}^{\mathrm{7}} \left({x}\right)}{{x}^{\mathrm{7}} }{dx} \\ $$

Question Number 83361 Answers: 1 Comments: 1

lim_(x→0^+ ) ((1−cos (x))/(√x)) =

$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{x}\right)}{\sqrt{\mathrm{x}}}\:=\: \\ $$

Question Number 83354 Answers: 0 Comments: 2

Question Number 83352 Answers: 1 Comments: 6

(√(2sin^2 ((x/2))(1−cos (x)))) = −sin (−x)−5cos (x)

$$\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{x}}{\mathrm{2}}\right)\left(\mathrm{1}−\mathrm{cos}\:\left(\mathrm{x}\right)\right)}\:=\:−\mathrm{sin}\:\left(−\mathrm{x}\right)−\mathrm{5cos}\:\left(\mathrm{x}\right) \\ $$

Question Number 83342 Answers: 1 Comments: 0

∫_0 ^1 ∫_0 ^( z) ∫_y ^1 ((z^(n+1) Li_1 (y))/((zx)^2 ))dx dy dz , ∀ n∈z

$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\:{z}} \int_{{y}} ^{\mathrm{1}} \frac{{z}^{{n}+\mathrm{1}} {Li}_{\mathrm{1}} \left({y}\right)}{\left({zx}\right)^{\mathrm{2}} }{dx}\:{dy}\:{dz}\:,\:\forall\:{n}\in{z} \\ $$

Question Number 83341 Answers: 1 Comments: 1

Find the maximum and minimum of the expression 𝚺_(i=1) ^n a_i x_i with 𝚺_(i=1) ^n (x_i −b_i )^2 =c^2 , where a_i , b_i and c are constants. (extracted and modified from Q83331)

$${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${of}\:{the}\:{expression}\:\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}{a}}_{\boldsymbol{{i}}} \boldsymbol{{x}}_{\boldsymbol{{i}}} \:{with} \\ $$$$\underset{\boldsymbol{{i}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}}\left(\boldsymbol{{x}}_{\boldsymbol{{i}}} −\boldsymbol{{b}}_{\boldsymbol{{i}}} \right)^{\mathrm{2}} =\boldsymbol{{c}}^{\mathrm{2}} ,\:{where}\:\boldsymbol{{a}}_{\boldsymbol{{i}}} ,\:\boldsymbol{{b}}_{\boldsymbol{{i}}} \:{and}\:\boldsymbol{{c}}\:{are} \\ $$$${constants}. \\ $$$$ \\ $$$$\left({extracted}\:{and}\:{modified}\:{from}\:{Q}\mathrm{83331}\right) \\ $$

Question Number 83340 Answers: 0 Comments: 0

by using the lagrange method solve the partial equatio (p−q=(z/(x+y)))

$${by}\:{using}\:{the}\:{lagrange}\:{method}\:{solve}\:{the}\:{partial}\:{equatio}\:\left({p}−{q}=\frac{{z}}{{x}+{y}}\right) \\ $$

Question Number 83338 Answers: 1 Comments: 0

∫ sin (3x) tan (2x) dx ?

$$\int\:\mathrm{sin}\:\left(\mathrm{3x}\right)\:\mathrm{tan}\:\left(\mathrm{2x}\right)\:\mathrm{dx}\:? \\ $$

Question Number 83331 Answers: 1 Comments: 7

Question Number 83329 Answers: 1 Comments: 1

lim_(x→0) (((e^(−2x) −(1+ax)))/(x^2 (1+bx))) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{e}^{−\mathrm{2x}} −\left(\mathrm{1}+\mathrm{ax}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:\left(\mathrm{1}+\mathrm{bx}\right)}\:=\:? \\ $$

Question Number 83327 Answers: 0 Comments: 2

(1−x^2 )(d^2 y/dx^2 ) −2x(dy/dx) + p(p+1)y = 0 in descending power of x. what is the solution?

$$\left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:−\mathrm{2x}\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\mathrm{p}\left(\mathrm{p}+\mathrm{1}\right)\mathrm{y}\:=\:\mathrm{0}\: \\ $$$$\mathrm{in}\:\mathrm{descending}\:\mathrm{power}\:\mathrm{of}\:\mathrm{x}.\:\mathrm{what}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{solution}? \\ $$

Question Number 83323 Answers: 1 Comments: 1

lim_(x→∞) (√((3x−2)(x−(√2)))) − x(√3)−(√2) =?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\left(\mathrm{3x}−\mathrm{2}\right)\left(\mathrm{x}−\sqrt{\mathrm{2}}\right)}\:−\:\mathrm{x}\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}\:=? \\ $$$$ \\ $$

Question Number 83319 Answers: 1 Comments: 0

if tan β = ((tan α + tan γ)/(1+tan αtan γ)) show that sin 2β = ((sin 2α+sin 2γ)/(1+sin 2αsin 2γ))

$$\mathrm{if}\:\mathrm{tan}\:\beta\:=\:\frac{\mathrm{tan}\:\alpha\:+\:\mathrm{tan}\:\gamma}{\mathrm{1}+\mathrm{tan}\:\alpha\mathrm{tan}\:\gamma} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{sin}\:\mathrm{2}\beta\:=\:\frac{\mathrm{sin}\:\mathrm{2}\alpha+\mathrm{sin}\:\mathrm{2}\gamma}{\mathrm{1}+\mathrm{sin}\:\mathrm{2}\alpha\mathrm{sin}\:\mathrm{2}\gamma} \\ $$

Question Number 83318 Answers: 0 Comments: 0

Evaluate ∫x^(1/x^n ) dx ,n>0

$${Evaluate} \\ $$$$\int{x}^{\frac{\mathrm{1}}{{x}^{{n}} }} \:{dx}\:,{n}>\mathrm{0} \\ $$

Question Number 83307 Answers: 0 Comments: 4

Question Number 83297 Answers: 1 Comments: 1

Write down a series expansion for ln [((1−2x)/((1+2x)^2 ))] in ascending powers of x up to and including the term in x^4 . if x is small that terms in x^2 and higher powers are negleted show that (((1−2x)/(1+2x)))^(1/(2x)) ≅ (1 + x)e^(−3)

$$\mathrm{Write}\:\mathrm{down}\:\mathrm{a}\:\mathrm{series}\:\mathrm{expansion}\:\mathrm{for}\: \\ $$$$\:\mathrm{ln}\:\left[\frac{\mathrm{1}−\mathrm{2}{x}}{\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} }\right]\:\mathrm{in}\:\mathrm{ascending}\:\mathrm{powers}\:\mathrm{of}\:\mathrm{x}\: \\ $$$$\mathrm{up}\:\mathrm{to}\:\mathrm{and}\:\mathrm{including}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{4}} .\: \\ $$$$\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{small}\:\mathrm{that}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{higher}\:\mathrm{powers} \\ $$$$\mathrm{are}\:\mathrm{negleted}\:\mathrm{show}\:\mathrm{that}\:\:\:\left(\frac{\mathrm{1}−\mathrm{2}{x}}{\mathrm{1}+\mathrm{2}{x}}\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}}} \:\cong\:\left(\mathrm{1}\:+\:{x}\right){e}^{−\mathrm{3}} \\ $$$$ \\ $$

Question Number 83296 Answers: 0 Comments: 2

Obtain a maclaurin expansion for a) e^(cos x ) b) e^(cos^2 x)

$$\mathrm{Obtain}\:\mathrm{a}\:\mathrm{maclaurin}\:\mathrm{expansion}\:\mathrm{for}\: \\ $$$$\left.\mathrm{a}\left.\right)\:\mathrm{e}^{\mathrm{cos}\:{x}\:} \:\:\:\:\:\:\:\:\mathrm{b}\right)\:\mathrm{e}^{\mathrm{cos}\:^{\mathrm{2}} {x}} \\ $$

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