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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

Question Number 102347 Answers: 2 Comments: 2

Question Number 102341 Answers: 4 Comments: 0

∫((xdx)/((1+x^2 )(√(1−x^2 ))))

$$\int\frac{\mathrm{xdx}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }} \\ $$

Question Number 102342 Answers: 2 Comments: 2

If { ((x=2t+sin 2t)),((y=e^(sin 2t) )) :} prove that (1/y).(dy/dx) = tan ((π/4)−t)

$${If}\:\begin{cases}{{x}=\mathrm{2}{t}+\mathrm{sin}\:\mathrm{2}{t}}\\{{y}={e}^{\mathrm{sin}\:\mathrm{2}{t}} }\end{cases} \\ $$$${prove}\:{that}\:\frac{\mathrm{1}}{{y}}.\frac{{dy}}{{dx}}\:=\:\mathrm{tan}\:\left(\frac{\pi}{\mathrm{4}}−{t}\right) \\ $$

Question Number 102336 Answers: 1 Comments: 1

if f(x)≤2l +1 and ∫_1 ^3 f(x)dx≤l^2 find the value of l

$${if}\:\:{f}\left({x}\right)\leqslant\mathrm{2}{l}\:+\mathrm{1}\: \\ $$$${and}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} {f}\left({x}\right){dx}\leqslant{l}^{\mathrm{2}} \\ $$$${find}\:{the}\:{value}\:{of}\:{l} \\ $$

Question Number 102366 Answers: 3 Comments: 0

∫_0 ^(π/2) ((cos x)/(1+cos x+sin x)) dx ?

$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}+\mathrm{cos}\:{x}+\mathrm{sin}\:{x}}\:{dx}\:? \\ $$

Question Number 102303 Answers: 2 Comments: 1

∫ ((1+csc 2x)/(1−sin 2x)) dx ?

$$\int\:\frac{\mathrm{1}+\mathrm{csc}\:\mathrm{2}{x}}{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}\:{dx}\:? \\ $$

Question Number 102301 Answers: 0 Comments: 6

to all friends in this forum. i′ll be off for a while . thank you for the discussion in this forum . see you another time. (JS ⊛)

$${to}\:{all}\:{friends}\:{in}\:{this}\:{forum}. \\ $$$${i}'{ll}\:{be}\:{off}\:{for}\:{a}\:{while}\:.\:{thank}\:{you} \\ $$$${for}\:{the}\:{discussion}\:{in}\:{this}\:{forum} \\ $$$$.\:{see}\:{you}\:{another}\:{time}.\:\left({JS}\:\circledast\right) \\ $$

Question Number 102298 Answers: 1 Comments: 0

sinx∙(dy/dx)−ycosx=y^3 sin^2 xcosx

$$\mathrm{sinx}\centerdot\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{ycosx}=\mathrm{y}^{\mathrm{3}} \mathrm{sin}^{\mathrm{2}} \mathrm{xcosx} \\ $$

Question Number 102296 Answers: 1 Comments: 0

lim_(t→∞) (1/t) ∫_0 ^t sin (αx) cos (βx) dx

$$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{t}}\:\underset{\mathrm{0}} {\overset{{t}} {\int}}\:\mathrm{sin}\:\left(\alpha{x}\right)\:\mathrm{cos}\:\left(\beta{x}\right)\:{dx} \\ $$

Question Number 102295 Answers: 0 Comments: 0

Solve the equation : (x^2 lny−x)y′=y

$$\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{equation}}\:: \\ $$$$\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} \boldsymbol{\mathrm{lny}}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}}'=\boldsymbol{\mathrm{y}} \\ $$

Question Number 102330 Answers: 0 Comments: 0

Do this integration(please do it step by step and write the used formula) ∫(1/2)(sin x)(e^(sin x) )dx

$${Do}\:{this}\:{integration}\left({please}\:{do}\:{it}\:{step}\:{by}\:{step}\:{and}\:{write}\:{the}\:{used}\:{formula}\right) \\ $$$$\int\frac{\mathrm{1}}{\mathrm{2}}\left({sin}\:{x}\right)\left({e}^{{sin}\:{x}} \right){dx} \\ $$

Question Number 102329 Answers: 0 Comments: 0

Question Number 102328 Answers: 1 Comments: 0

Question Number 102292 Answers: 1 Comments: 0

Question Number 102283 Answers: 3 Comments: 0

sinx(dy/dx)−2ycosx=3sinx

$$\mathrm{sinx}\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{2ycosx}=\mathrm{3sinx} \\ $$

Question Number 102278 Answers: 3 Comments: 4

Find the greatest coefficient in the following without actually expand. (i) (5 − 3x)^(10) (ii) (5 + 3x)^(− 10)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{without} \\ $$$$\mathrm{actually}\:\mathrm{expand}. \\ $$$$\left(\mathrm{i}\right)\:\:\:\:\:\:\:\:\left(\mathrm{5}\:\:−\:\:\mathrm{3x}\right)^{\mathrm{10}} \\ $$$$\left(\mathrm{ii}\right)\:\:\:\:\:\:\:\:\left(\mathrm{5}\:\:+\:\:\mathrm{3x}\right)^{−\:\mathrm{10}} \\ $$

Question Number 102275 Answers: 0 Comments: 2

∫_1 ^2 ln(((x^4 + 4)/(x^2 + 4)))(dx/x)

$$\int_{\mathrm{1}} ^{\mathrm{2}} \:\boldsymbol{{ln}}\left(\frac{\boldsymbol{{x}}^{\mathrm{4}} \:+\:\mathrm{4}}{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\mathrm{4}}\right)\frac{\boldsymbol{{dx}}}{\boldsymbol{{x}}} \\ $$

Question Number 102269 Answers: 1 Comments: 0

if P_2 ^( n−m) =72 and P_2 ^( n+m) =210 find the value of m and n ?

$${if}\:{P}_{\mathrm{2}} ^{\:{n}−{m}} =\mathrm{72}\:\:{and}\:{P}_{\mathrm{2}} ^{\:{n}+{m}} =\mathrm{210}\:{find}\:{the}\:{value}\:{of}\:{m}\:{and}\:{n}\:? \\ $$

Question Number 102268 Answers: 0 Comments: 0

Question Number 102260 Answers: 2 Comments: 2

Question Number 102243 Answers: 1 Comments: 0

At examination, a student most answer to 8 question betwen a total of 10 question. 1) How many many choices is possible? 2)How many choices is possible if a student most answer to 3 questions at least? 3)How many choices is possible if a student most answer to at least 4 questions of the five first questions?

$${At}\:{examination},\:{a}\:{student}\:{most} \\ $$$${answer}\:{to}\:\mathrm{8}\:{question}\:{betwen}\:{a}\:{total} \\ $$$${of}\:\mathrm{10}\:{question}. \\ $$$$\left.\mathrm{1}\right)\:{How}\:{many}\:{many}\:{choices}\:{is}\: \\ $$$${possible}? \\ $$$$\left.\mathrm{2}\right){How}\:{many}\:{choices}\:{is}\:{possible}\:{if}\:{a} \\ $$$${student}\:{most}\:{answer}\:{to}\:\mathrm{3}\:{questions} \\ $$$${at}\:{least}? \\ $$$$\left.\mathrm{3}\right){How}\:{many}\:{choices}\:{is}\:{possible}\:{if}\:{a} \\ $$$${student}\:{most}\:{answer}\:{to}\:{at}\:{least}\:\mathrm{4} \\ $$$${questions}\:{of}\:\:{the}\:{five}\:{first}\:{questions}? \\ $$

Question Number 102241 Answers: 2 Comments: 3

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