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AllQuestion and Answers: Page 12

Question Number 224207    Answers: 0   Comments: 5

Question Number 224203    Answers: 0   Comments: 6

Question Number 224201    Answers: 0   Comments: 0

∫ (x^3 /(x^7 −8x^2 )) dx

$$\int\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{7}} −\mathrm{8x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 224191    Answers: 0   Comments: 1

Question Number 224197    Answers: 2   Comments: 0

∫_0 ^∞ (e^(−𝛟x^2 ) +e^(−𝛅x^2 ) +e^(−𝛄x^2 ) ) 𝛄−euler′s mascheroni constant 𝛟−golden ratio 𝛅−silver ratio klipto−quanta♠

$$\int_{\mathrm{0}} ^{\infty} \left(\boldsymbol{\mathrm{e}}^{−\boldsymbol{\varphi\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\delta\mathrm{x}}^{\mathrm{2}} } +\boldsymbol{\mathrm{e}}^{−\boldsymbol{\gamma\mathrm{x}}^{\mathrm{2}} } \right) \\ $$$$\boldsymbol{\gamma}−\boldsymbol{\mathrm{euler}}'\boldsymbol{\mathrm{s}}\:\boldsymbol{\mathrm{mascheroni}}\:\boldsymbol{\mathrm{constant}} \\ $$$$\boldsymbol{\varphi}−\boldsymbol{\mathrm{golden}}\:\boldsymbol{\mathrm{ratio}} \\ $$$$\boldsymbol{\delta}−\boldsymbol{\mathrm{silver}}\:\boldsymbol{\mathrm{ratio}} \\ $$$$\boldsymbol{\mathrm{klipto}}−\boldsymbol{\mathrm{quanta}}\spadesuit \\ $$

Question Number 224182    Answers: 1   Comments: 0

Calculate I=∫ ((sin x)/(1+ sin x)) dx

$$\mathrm{Calculate} \\ $$$${I}=\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\:\mathrm{sin}\:{x}}\:\mathrm{d}{x} \\ $$

Question Number 224176    Answers: 2   Comments: 1

Question Number 224168    Answers: 2   Comments: 1

Question Number 224160    Answers: 0   Comments: 0

Q224122

$${Q}\mathrm{224122} \\ $$

Question Number 224153    Answers: 0   Comments: 8

Question Number 224150    Answers: 0   Comments: 2

Question Number 224146    Answers: 1   Comments: 0

a = 12^(223) ∙ 7^(56) + 19^(25) what is the last digit of the number?

$$\boldsymbol{\mathrm{a}}\:=\:\mathrm{12}^{\mathrm{223}} \:\centerdot\:\mathrm{7}^{\mathrm{56}} \:+\:\mathrm{19}^{\mathrm{25}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}? \\ $$

Question Number 224144    Answers: 1   Comments: 1

Question Number 224124    Answers: 2   Comments: 0

∫_(−2) ^2 ((x^3 cos((x/2))+(1/2))/( (√(4−x^2 ))))

$$\int_{−\mathrm{2}} ^{\mathrm{2}} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{3}} \boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}}{\:\sqrt{\mathrm{4}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }} \\ $$

Question Number 224122    Answers: 1   Comments: 1

Question Number 224121    Answers: 1   Comments: 0

Question Number 224118    Answers: 1   Comments: 0

Question Number 224113    Answers: 0   Comments: 0

Guys my exams are finished ! I will be active as usual! :)

$${Guys}\:{my}\:{exams}\:{are}\:{finished}\:! \\ $$$${I}\:{will}\:{be}\:{active}\:{as}\:{usual}! \\ $$$$\left.:\right) \\ $$

Question Number 224108    Answers: 3   Comments: 0

Question Number 224106    Answers: 0   Comments: 1

Question Number 224100    Answers: 1   Comments: 0

Calculate I=∫^( +∞) _( 0) [(1/t)−(1/(sh(t)))]^( 2) dt

$$\mathrm{Calculate}\:\mathrm{I}=\underset{\:\mathrm{0}} {\int}^{\:+\infty} \left[\frac{\mathrm{1}}{\mathrm{t}}−\frac{\mathrm{1}}{\mathrm{sh}\left(\mathrm{t}\right)}\right]^{\:\mathrm{2}} \mathrm{dt} \\ $$

Question Number 224095    Answers: 1   Comments: 2

how to prove that x + 9 = x is not has solution because (x + 9)^2 = x^2 x^2 + 18x + 81 = x^2 18x = −81 x = − ((81)/(18)) = −(9/2)

$${how}\:{to}\:{prove}\:{that}\:\:{x}\:+\:\mathrm{9}\:=\:{x}\:{is}\:{not}\:{has}\:{solution} \\ $$$${because}\: \\ $$$$\left({x}\:+\:\mathrm{9}\right)^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} \:+\:\mathrm{18}{x}\:+\:\mathrm{81}\:=\:{x}^{\mathrm{2}} \\ $$$$\mathrm{18}{x}\:=\:−\mathrm{81} \\ $$$${x}\:=\:−\:\frac{\mathrm{81}}{\mathrm{18}}\:=\:−\frac{\mathrm{9}}{\mathrm{2}} \\ $$

Question Number 224092    Answers: 0   Comments: 3

what′s the matter? yesterday the app was not accessible for many hours. now it seems to work normally again. but actually it doesn′t, at least with me. when i tip “view older” to scroll through the old posts, the app crashes always at some point, showing a message “Math Editor isn′t responding. × Close it ⊝ Wait” are you also experiencing the same problem? what has happened since yesterday?

$${what}'{s}\:{the}\:{matter}? \\ $$$${yesterday}\:{the}\:{app}\:{was}\:{not}\:{accessible} \\ $$$${for}\:{many}\:{hours}.\:{now}\:{it}\:{seems}\:{to} \\ $$$${work}\:{normally}\:{again}.\:{but}\:{actually} \\ $$$${it}\:{doesn}'{t},\:{at}\:{least}\:{with}\:{me}.\:{when} \\ $$$${i}\:{tip}\:``\boldsymbol{{view}}\:\boldsymbol{{older}}''\:{to}\:{scroll}\:{through} \\ $$$${the}\:{old}\:{posts},\:{the}\:{app}\:{crashes}\:{always} \\ $$$${at}\:{some}\:{point},\:{showing}\:{a}\:{message} \\ $$$$``{Math}\:{Editor}\:{isn}'{t}\:{responding}. \\ $$$$×\:{Close}\:{it} \\ $$$$\circleddash\:{Wait}'' \\ $$$${are}\:{you}\:{also}\:{experiencing}\:{the}\:{same} \\ $$$${problem}?\: \\ $$$${what}\:{has}\:{happened}\:{since}\:{yesterday}? \\ $$

Question Number 224085    Answers: 2   Comments: 0

If f(x)=4x^3 +3x^2 +x, Then solve for a and b: max_(x∈R) {∫_x ^2 f(t)dt}=a where x=b

$$\mathrm{If}\:{f}\left({x}\right)=\mathrm{4}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} +{x},\:\mathrm{Then}\:\mathrm{solve}\:\mathrm{for}\:{a}\:\mathrm{and}\:{b}: \\ $$$$\underset{{x}\in\mathbb{R}} {\mathrm{max}}\left\{\int_{{x}} ^{\mathrm{2}} {f}\left({t}\right){dt}\right\}={a}\:\mathrm{where}\:{x}={b} \\ $$

Question Number 224080    Answers: 0   Comments: 0

Use choleski′s method to solve the following system of equation 4x_1 −2x_2 +2x_3 =6 4x_1 −3x_2 −2x_3 =−8 2x_1 +3x_2 −x_3 =5

$$\boldsymbol{{Use}}\:\boldsymbol{{choleski}}'\boldsymbol{{s}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\:\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{following}}\:\boldsymbol{{system}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{equation}} \\ $$$$\mathrm{4}\boldsymbol{{x}}_{\mathrm{1}} −\mathrm{2}\boldsymbol{{x}}_{\mathrm{2}} +\mathrm{2}\boldsymbol{{x}}_{\mathrm{3}} =\mathrm{6} \\ $$$$\mathrm{4}\boldsymbol{{x}}_{\mathrm{1}} −\mathrm{3}\boldsymbol{{x}}_{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}_{\mathrm{3}} =−\mathrm{8} \\ $$$$\mathrm{2}\boldsymbol{{x}}_{\mathrm{1}} +\mathrm{3}\boldsymbol{{x}}_{\mathrm{2}} −\boldsymbol{{x}}_{\mathrm{3}} =\mathrm{5} \\ $$

Question Number 224079    Answers: 0   Comments: 0

For the given function f(x),let x_0 =0,x_1 =0.6 and x_2 =0.9. construct the lagrange interpolating polynomials of degree. (1) at most 1 (2)at most 2 to approximate f(0.45) if (a) f(x)=cosx (b) f(x)=(√(1+x)) (c) f(x)=In(1+x) (d) f(x)=tanx

$$\boldsymbol{{For}}\:\boldsymbol{{the}}\:\boldsymbol{{given}}\:\boldsymbol{{function}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right),\boldsymbol{{let}}\:\boldsymbol{{x}}_{\mathrm{0}} =\mathrm{0},\boldsymbol{{x}}_{\mathrm{1}} =\mathrm{0}.\mathrm{6} \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{x}}_{\mathrm{2}} =\mathrm{0}.\mathrm{9}.\:\boldsymbol{{construct}}\:\boldsymbol{{the}}\:\boldsymbol{{lagrange}}\:\boldsymbol{{interpolating}} \\ $$$$\boldsymbol{{polynomials}}\:\boldsymbol{{of}}\:\boldsymbol{{degree}}.\:\left(\mathrm{1}\right)\:\boldsymbol{{at}}\:\boldsymbol{{most}}\:\mathrm{1}\:\left(\mathrm{2}\right)\boldsymbol{{at}}\:\boldsymbol{{most}}\:\mathrm{2} \\ $$$$\boldsymbol{{to}}\:\boldsymbol{{approximate}}\:\boldsymbol{{f}}\left(\mathrm{0}.\mathrm{45}\right)\:\boldsymbol{{if}}\: \\ $$$$\left(\boldsymbol{{a}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{cosx}}\:\:\left(\boldsymbol{{b}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\sqrt{\mathrm{1}+\boldsymbol{{x}}}\:\left(\boldsymbol{{c}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{In}}\left(\mathrm{1}+\boldsymbol{{x}}\right) \\ $$$$\left(\boldsymbol{{d}}\right)\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{tanx}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

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