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AllQuestion and Answers: Page 1149

Question Number 95982 Answers: 1 Comments: 0

Σx(y^3 −z^3 )=_____.

$$\Sigma{x}\left({y}^{\mathrm{3}} −{z}^{\mathrm{3}} \right)=\_\_\_\_\_. \\ $$

Question Number 95980 Answers: 1 Comments: 0

If lim_(x→3) (((√(3x+7))−((20x+4))^(1/(3 )) +ax+b)/((x−3)^2 )) exist , what is the value of ab

$$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\sqrt{\mathrm{3x}+\mathrm{7}}−\sqrt[{\mathrm{3}\:\:}]{\mathrm{20x}+\mathrm{4}}\:+{a}\mathrm{x}+{b}}{\left({x}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\mathrm{exist}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{ab}\: \\ $$

Question Number 95968 Answers: 1 Comments: 0

3^(((log _3 (2)+log _3 (3log _(1/3) (cot (π/3))))/(log _π (3).(log _2 (π)))) ? )

$$\mathrm{3}^{\frac{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{2}\right)+\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{3log}\:_{\frac{\mathrm{1}}{\mathrm{3}}} \left(\mathrm{cot}\:\frac{\pi}{\mathrm{3}}\right)\right)}{\mathrm{log}\:_{\pi} \left(\mathrm{3}\right).\left(\mathrm{log}\:_{\mathrm{2}} \left(\pi\right)\right)}\:?\:} \\ $$

Question Number 95964 Answers: 0 Comments: 0

{ ((x^2 +y^2 =13)),((2x^2 +3y=2xy^2 )) :}

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{13}}\\{\mathrm{2x}^{\mathrm{2}} +\mathrm{3y}=\mathrm{2xy}^{\mathrm{2}} }\end{cases} \\ $$

Question Number 95951 Answers: 4 Comments: 3

Question Number 95949 Answers: 2 Comments: 0

∫_0 ^(+∞) (x^2 /(e^x^2 −1))dx

$$\int_{\mathrm{0}} ^{+\infty} \frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } −\mathrm{1}}\mathrm{dx} \\ $$

Question Number 95943 Answers: 0 Comments: 0

f is a integrable function wich verify f(x+π)=f(x) prove that ∫_0 ^∞ f(x)×((sinx)/x)dx =∫_0 ^(π/2) f(x)dx

$$\mathrm{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{integrable}\:\mathrm{function}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{f}\left(\mathrm{x}+\pi\right)=\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\mathrm{f}\left(\mathrm{x}\right)×\frac{\mathrm{sinx}}{\mathrm{x}}\mathrm{dx}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 95966 Answers: 1 Comments: 0

find all pairs of integer for xy+3x−4y = 29

$$\mathrm{find}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{for}\: \\ $$$$\mathrm{xy}+\mathrm{3x}−\mathrm{4y}\:=\:\mathrm{29}\: \\ $$

Question Number 95967 Answers: 1 Comments: 1

Question Number 95933 Answers: 2 Comments: 2

y′′′+2y′−3y= e^x (x+3)

$$\mathrm{y}'''+\mathrm{2y}'−\mathrm{3y}=\:\mathrm{e}^{\mathrm{x}} \:\left(\mathrm{x}+\mathrm{3}\right)\: \\ $$

Question Number 95924 Answers: 1 Comments: 1

form a Lagrangian to maximize x^2 −y^2 subject to the constraint 2x+y = 3?

$$\mathrm{form}\:\mathrm{a}\:\mathrm{Lagrangian}\:\mathrm{to}\:\mathrm{maximize} \\ $$$$\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} \:\mathrm{subject}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{constraint}\:\mathrm{2x}+\mathrm{y}\:=\:\mathrm{3}? \\ $$

Question Number 95920 Answers: 3 Comments: 0

((54+(√x)))^(1/(3 )) + ((54−(√x)))^(1/(3 )) = ((18))^(1/(3 )) x = ?

$$\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}+\sqrt{\mathrm{x}}}\:+\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{54}−\sqrt{\mathrm{x}}}\:=\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{18}}\: \\ $$$$\mathrm{x}\:=\:?\: \\ $$

Question Number 95919 Answers: 1 Comments: 0

∫3^(−4x^2 ) dx=? (0,∞)

$$ \\ $$$$\int\mathrm{3}^{−\mathrm{4x}^{\mathrm{2}} } \mathrm{dx}=?\:\:\:\:\left(\mathrm{0},\infty\right) \\ $$

Question Number 95941 Answers: 0 Comments: 0

prove that (1/(sinx)) =Σ_(n=−∞) ^(+∞) (((−1)^n )/(x+nπ))

$$\mathrm{prove}\:\mathrm{that}\:\frac{\mathrm{1}}{\mathrm{sinx}}\:=\sum_{\mathrm{n}=−\infty} ^{+\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{x}+\mathrm{n}\pi} \\ $$

Question Number 95912 Answers: 0 Comments: 2

(((2n)),(n) ) = 20 find n?

$$\begin{pmatrix}{\mathrm{2n}}\\{\mathrm{n}}\end{pmatrix}\:=\:\mathrm{20}\: \\ $$$$\mathrm{find}\:\mathrm{n}? \\ $$

Question Number 95903 Answers: 2 Comments: 3

Question Number 95901 Answers: 1 Comments: 0

(1/(998!)) + (1/(999!)) = (x^3 /(100!))

$$\frac{\mathrm{1}}{\mathrm{998}!}\:+\:\frac{\mathrm{1}}{\mathrm{999}!}\:=\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{100}!}\: \\ $$

Question Number 95898 Answers: 0 Comments: 0

x^2 +xy+(y^3 /3)=25 (y^2 /3)+z^2 =9 z^2 +zx+x^2 =16 so xy+2yz+3zx=?

$${x}^{\mathrm{2}} +{xy}+\frac{{y}^{\mathrm{3}} }{\mathrm{3}}=\mathrm{25} \\ $$$$\frac{{y}^{\mathrm{2}} }{\mathrm{3}}+{z}^{\mathrm{2}} =\mathrm{9} \\ $$$${z}^{\mathrm{2}} +{zx}+{x}^{\mathrm{2}} =\mathrm{16} \\ $$$${so}\:{xy}+\mathrm{2}{yz}+\mathrm{3}{zx}=? \\ $$

Question Number 95897 Answers: 2 Comments: 0

If x∈C . find solution of 3+i(√2) = e^(ix)

$$\mathrm{If}\:{x}\in\mathbb{C}\:.\:\mathrm{find}\:\mathrm{solution}\:\mathrm{of}\: \\ $$$$\mathrm{3}+{i}\sqrt{\mathrm{2}}\:=\:{e}^{{ix}} \: \\ $$

Question Number 95888 Answers: 1 Comments: 0

(1−2x)^5 (2+x)^6 = a+bx+cx^2 +dx^3 +... find : a,b,c and d

$$\left(\mathrm{1}−\mathrm{2x}\right)^{\mathrm{5}} \left(\mathrm{2}+\mathrm{x}\right)^{\mathrm{6}} =\:\mathrm{a}+\mathrm{bx}+\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}^{\mathrm{3}} +... \\ $$$$\mathrm{find}\::\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{and}\:\mathrm{d}\: \\ $$

Question Number 96026 Answers: 0 Comments: 1

sin (p/x)=1

$$\mathrm{sin}\:\frac{\mathrm{p}}{\mathrm{x}}=\mathrm{1} \\ $$

Question Number 95860 Answers: 1 Comments: 0

A^− ∙(B+B^− )∙(C+C^− )∙(D+D^− )

$$\overset{−} {{A}}\centerdot\left({B}+\overset{−} {{B}}\right)\centerdot\left({C}+\overset{−} {{C}}\right)\centerdot\left({D}+\overset{−} {{D}}\right) \\ $$

Question Number 95849 Answers: 2 Comments: 0

lim_(n→∞) (1/(n+1)) + (1/(n+2)) + (1/(n+3)) + ... + (1/(n+n))??

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{3}}\:+\:...\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{n}}?? \\ $$

Question Number 95848 Answers: 4 Comments: 0

∫_0 ^(π/2) (dx/(√(1+sin x))) ?

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

Question Number 95845 Answers: 1 Comments: 0

calculate ∫_0 ^1 (−1)^([(2/x)]) dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(−\mathrm{1}\right)^{\left[\frac{\mathrm{2}}{\mathrm{x}}\right]} \:\mathrm{dx} \\ $$

Question Number 95844 Answers: 2 Comments: 0

cacuate ∫_(−(π/4)) ^(π/4) ln(1+a cos^2 t)dt with ∣a∣<1

$$\mathrm{cacuate}\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{ln}\left(\mathrm{1}+\mathrm{a}\:\mathrm{cos}^{\mathrm{2}} \mathrm{t}\right)\mathrm{dt}\:\mathrm{with}\:\mid\mathrm{a}\mid<\mathrm{1} \\ $$

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