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AllQuestion and Answers: Page 285

Question Number 192720 Answers: 4 Comments: 0

Question Number 192715 Answers: 1 Comments: 0

∫(dx/(x^2 (√(x^2 +a^2 ))))=?

$$\int\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{a}^{\mathrm{2}} }}=? \\ $$

Question Number 192712 Answers: 1 Comments: 0

∫_(−1/2) ^(1/2) (√(x^2 +1+(√(x^4 +x^2 +1)))) dx =?

$$\:\:\:\:\underset{−\mathrm{1}/\mathrm{2}} {\overset{\mathrm{1}/\mathrm{2}} {\int}}\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}+\sqrt{\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\mathrm{dx}\:=? \\ $$

Question Number 192707 Answers: 0 Comments: 0

Is been a while we hear from Mr. W (prof) hope he is fine by Gods grace

$$\:{Is}\:{been}\:{a}\:{while}\:{we}\:{hear}\:{from} \\ $$$$\:{Mr}.\:{W}\:\left({prof}\right)\:{hope}\:{he}\:{is}\:{fine}\:{by}\:{Gods} \\ $$$${grace} \\ $$

Question Number 192705 Answers: 0 Comments: 3

Question Number 192704 Answers: 2 Comments: 0

Question Number 192697 Answers: 1 Comments: 0

Find the value of (9x−(1/(100))x)^3 (9x−(2/(100))x)^3 (9x−(3/(100))x)^3 ...(9x−((2013)/(100))x)^3 .

$$\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\:\left(\mathrm{9x}−\frac{\mathrm{1}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{2}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} \left(\mathrm{9x}−\frac{\mathrm{3}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} ...\left(\mathrm{9x}−\frac{\mathrm{2013}}{\mathrm{100}}\mathrm{x}\right)^{\mathrm{3}} . \\ $$

Question Number 192689 Answers: 2 Comments: 1

a plant grow up 1.67cm in the first week after that it grow up 4% grow up more than the first week every week, how much will grow up in 11th week?

$${a}\:{plant}\:{grow}\:{up}\:\mathrm{1}.\mathrm{67}{cm}\:{in}\:{the}\:{first}\:{week} \\ $$$${after}\:{that}\:{it}\:{grow}\:{up}\:\mathrm{4\%}\:{grow}\:{up}\:{more} \\ $$$${than}\:{the}\:{first}\:{week}\:{every}\:{week},\:{how}\:{much} \\ $$$${will}\:{grow}\:{up}\:{in}\:\mathrm{11}{th}\:{week}? \\ $$

Question Number 192688 Answers: 1 Comments: 0

Prove that : C_n ^k = (1/(2π)) ∫^( π) _( −π) (2cos(θ/2))^n cos[((n/2)−k)θ]dθ

$$\mathrm{Prove}\:\mathrm{that}\:: \\ $$$$\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \:=\:\frac{\mathrm{1}}{\mathrm{2}\pi}\:\underset{\:−\pi} {\int}^{\:\:\:\pi} \left(\mathrm{2cos}\frac{\theta}{\mathrm{2}}\right)^{\mathrm{n}} \mathrm{cos}\left[\left(\frac{\mathrm{n}}{\mathrm{2}}−\mathrm{k}\right)\theta\right]\mathrm{d}\theta \\ $$

Question Number 192687 Answers: 1 Comments: 0

(1/π)∫_0 ^(2π) xcos(nx)dx Help!

$$\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\mathrm{2}\pi} \mathrm{xcos}\left(\mathrm{nx}\right)\mathrm{dx} \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 192676 Answers: 1 Comments: 0

Find: x = ? 1. lg(5x^2 − 6)∙lg(5x − 6) = 0 2. (2x − 5)∙log_3 (1,5 − x) = 0 3. 4^x − 14∙2^x − 32 = 0

$$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$$$\mathrm{1}.\:\:\mathrm{lg}\left(\mathrm{5x}^{\mathrm{2}} \:−\:\mathrm{6}\right)\centerdot\mathrm{lg}\left(\mathrm{5x}\:−\:\mathrm{6}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{2}.\:\:\left(\mathrm{2x}\:−\:\mathrm{5}\right)\centerdot\mathrm{log}_{\mathrm{3}} \left(\mathrm{1},\mathrm{5}\:−\:\mathrm{x}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{3}.\:\:\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{14}\centerdot\mathrm{2}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{32}\:=\:\mathrm{0} \\ $$

Question Number 192675 Answers: 1 Comments: 0

Question Number 192668 Answers: 2 Comments: 0

∫_0 ^4 (1/x)e^x dx − ∫_0 ^4 (1/x)e^((1/2)x) dx= ?

$$\int_{\mathrm{0}} ^{\mathrm{4}} \frac{\mathrm{1}}{{x}}{e}^{{x}} {dx}\:−\:\int_{\mathrm{0}} ^{\mathrm{4}} \frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{1}}{\mathrm{2}}{x}} {dx}=\:? \\ $$

Question Number 192664 Answers: 0 Comments: 0

Question Number 192663 Answers: 1 Comments: 0

Question Number 192661 Answers: 1 Comments: 2

Question Number 192652 Answers: 2 Comments: 0

lim_(x→0) ((1−(√(cos(x))))/(1+cos((√x))))

$${lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{1}−\sqrt{{cos}\left({x}\right)}}{\mathrm{1}+{cos}\left(\sqrt{{x}}\right)} \\ $$

Question Number 192651 Answers: 2 Comments: 0

lim_(x→0) ((2−(√(cos(x)))−cos(x))/x^2 )

$$ \\ $$$${lim}_{{x}\rightarrow\mathrm{0}} \frac{\mathrm{2}−\sqrt{{cos}\left({x}\right)}−{cos}\left({x}\right)}{{x}^{\mathrm{2}} } \\ $$

Question Number 192650 Answers: 2 Comments: 0

lim_(x→0) ((x−sen(x))/(tan^3 (x))) without lhopital rule

$$ \\ $$$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} \frac{{x}−{sen}\left({x}\right)}{{tan}^{\mathrm{3}} \left({x}\right)} \\ $$$${without}\:{lhopital}\:{rule} \\ $$

Question Number 192648 Answers: 1 Comments: 0

find g(f(x)) f(x)=x^3 −x^2 +3x g(x)=x^2 −2x+1

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)\right) \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$$$\boldsymbol{\mathrm{g}}\left(\boldsymbol{\mathrm{x}}\right)=\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1} \\ $$

Question Number 192646 Answers: 1 Comments: 0

lim_(x⇒3) (√((x^2 −4x+3)/(x−3))) find the limit

$$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\Rightarrow\mathrm{3}} \sqrt{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{3}}{\boldsymbol{\mathrm{x}}−\mathrm{3}}} \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{limit}} \\ $$

Question Number 192639 Answers: 2 Comments: 0

lim_(x⇒∝ ) ((3x^3 +3x^2 +1)/(5x^3 +4x^2 +x)) find the limit

$$ \\ $$lim_(x⇒∝ ) ((3x^3 +3x^2 +1)/(5x^3 +4x^2 +x)) find the limit

Question Number 192636 Answers: 1 Comments: 0

lim_(x→1 ) (3x^2 −7x+3)^(10) find the limit

$${lim}_{{x}\rightarrow\mathrm{1}\:} \left(\mathrm{3}{x}^{\mathrm{2}} \:−\mathrm{7}{x}+\mathrm{3}\right)^{\mathrm{10}} \: \\ $$$${find}\:{the}\:{limit} \\ $$

Question Number 192634 Answers: 1 Comments: 0

∫sin(12x +8 )dx

$$\int\boldsymbol{{sin}}\left(\mathrm{12}{x}\:+\mathrm{8}\:\right){dx} \\ $$

Question Number 192630 Answers: 0 Comments: 0

z=xy−5x+2y. find (dz/dx) and (dz/dy) at(2,4)

$${z}={xy}−\mathrm{5}{x}+\mathrm{2}{y}.\:{find}\:\frac{{dz}}{{dx}}\:{and}\:\frac{{dz}}{{dy}}\:{at}\left(\mathrm{2},\mathrm{4}\right) \\ $$

Question Number 192629 Answers: 0 Comments: 0

Z=f(x_(1,) x_(2,) x_3 )=x_1 x_2 +x_1 ^5 −x_2 ^2 x_3 find f_1 ,f_(11) ,and f_(21)

$${Z}={f}\left({x}_{\mathrm{1},} {x}_{\mathrm{2},} {x}_{\mathrm{3}} \right)={x}_{\mathrm{1}} {x}_{\mathrm{2}} +{x}_{\mathrm{1}} ^{\mathrm{5}} −{x}_{\mathrm{2}} ^{\mathrm{2}} {x}_{\mathrm{3}} \:{find}\:{f}_{\mathrm{1}} ,{f}_{\mathrm{11}} ,{and}\:{f}_{\mathrm{21}} \\ $$

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