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Question Number 203875 Answers: 1 Comments: 0

Hmmm..... I have one Question. f(t)∈C^∞ , {C_ ^𝛂 mean can derivate 𝛂 times.} where t∈R , Can f(t) integrable when S∈R\{Q}?? Ex. integral ∫_1 ^( e) ln(z)dz S∈[1,e] But Except Q in set S like.. S^′ =S\{Q} than Can integrable In S′

$$\mathrm{Hmmm}.....\:\mathrm{I}\:\mathrm{have}\:\mathrm{one}\:\mathrm{Question}. \\ $$$${f}\left({t}\right)\in{C}^{\infty} \:,\:\left\{{C}_{\:} ^{\boldsymbol{\alpha}} \:\mathrm{mean}\:\mathrm{can}\:\mathrm{derivate}\:\boldsymbol{\alpha}\:\mathrm{times}.\right\} \\ $$$$\mathrm{where}\:{t}\in\mathbb{R}\:,\:\mathrm{Can}\:{f}\left({t}\right)\:\:\mathrm{integrable}\:\mathrm{when}\:{S}\in\mathbb{R}\backslash\left\{\mathbb{Q}\right\}?? \\ $$$$\mathrm{Ex}.\:\mathrm{integral}\:\int_{\mathrm{1}} ^{\:{e}} \:\mathrm{ln}\left({z}\right)\mathrm{d}{z}\:{S}\in\left[\mathrm{1},{e}\right]\: \\ $$$$\mathrm{But}\:\mathrm{Except}\:\mathbb{Q}\:\mathrm{in}\:\mathrm{set}\:{S}\:\mathrm{like}..\:{S}^{'} ={S}\backslash\left\{\mathbb{Q}\right\}\: \\ $$$$\mathrm{than}\:\mathrm{Can}\:\mathrm{integrable}\:\mathrm{In}\:{S}' \\ $$

Question Number 203867 Answers: 1 Comments: 0

find ∫(√((1−x^3 )/(1+x^3 )))dx

$${find}\:\int\sqrt{\frac{\mathrm{1}−{x}^{\mathrm{3}} }{\mathrm{1}+{x}^{\mathrm{3}} }}{dx} \\ $$

Question Number 203859 Answers: 0 Comments: 3

Show that the surface z = xy has neither a maximum nor a minimum point

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{surface}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{z}\:=\:\mathrm{xy} \\ $$$$\mathrm{has}\:\mathrm{neither}\:\mathrm{a}\:\mathrm{maximum}\:\mathrm{nor}\:\mathrm{a}\:\mathrm{minimum}\:\mathrm{point} \\ $$

Question Number 203858 Answers: 0 Comments: 1

Classsify the critical points of the function f(x,y) = x^2 y + (1/3)y^3 − x^2 − y^2 + 2 Thank you in advance!

$$\mathrm{Classsify}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{points}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\mathrm{x}^{\mathrm{2}} \mathrm{y}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{y}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{2} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{in}\:\mathrm{advance}! \\ $$

Question Number 203846 Answers: 1 Comments: 0

lim_(n→∞) Π_(i=2) ^n (((i^2 −1)/i^2 ))

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{i}=\mathrm{2}} {\overset{{n}} {\prod}}\left(\frac{{i}^{\mathrm{2}} −\mathrm{1}}{{i}^{\mathrm{2}} }\right) \\ $$

Question Number 203836 Answers: 2 Comments: 0

Question Number 203835 Answers: 2 Comments: 0

Question Number 203833 Answers: 1 Comments: 0

How many bit strings of length 11 have exactly three consecutive 1s?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{11}\:\mathrm{have} \\ $$$$\mathrm{exactly}\:\mathrm{three}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$

Question Number 203832 Answers: 2 Comments: 0

How many bit strings of length 10 do not have four consecutive 1s?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{bit}\:\mathrm{strings}\:\mathrm{of}\:\mathrm{length}\:\mathrm{10}\:\mathrm{do}\:\mathrm{not} \\ $$$$\mathrm{have}\:\mathrm{four}\:\mathrm{consecutive}\:\mathrm{1s}? \\ $$

Question Number 203826 Answers: 3 Comments: 0

Evaluate (26 + 15(√3))^(1/3) + (26 − 15(√3))^(1/3)

$${Evaluate} \\ $$$$\left(\mathrm{26}\:+\:\mathrm{15}\sqrt{\mathrm{3}}\right)^{\mathrm{1}/\mathrm{3}} +\:\left(\mathrm{26}\:−\:\mathrm{15}\sqrt{\mathrm{3}}\right)^{\mathrm{1}/\mathrm{3}} \\ $$

Question Number 203825 Answers: 1 Comments: 0

A sum of 2800 is invested, partly at 5% and partly at 4%. If the total income is 128 per annum, find the amount invested at 5%.

$${A}\:{sum}\:{of}\:\mathrm{2800}\:{is}\:{invested},\:{partly}\:{at}\:\mathrm{5\%} \\ $$$${and}\:{partly}\:{at}\:\mathrm{4\%}.\:{If}\:{the}\:{total}\:{income} \\ $$$${is}\:\mathrm{128}\:{per}\:{annum},\:{find}\:{the}\:{amount} \\ $$$${invested}\:{at}\:\mathrm{5\%}. \\ $$

Question Number 203822 Answers: 3 Comments: 0

Question Number 203819 Answers: 0 Comments: 0

((∣x^2 −3x∣)/(x^2 −9)) draw up the variaton table of this function

$$\frac{\mid{x}^{\mathrm{2}} −\mathrm{3}{x}\mid}{{x}^{\mathrm{2}} −\mathrm{9}}\:\:{draw}\:{up}\:{the}\:{variaton} \\ $$$${table}\:{of}\:{this}\:{function} \\ $$

Question Number 203809 Answers: 1 Comments: 0

x^3 +y^3 +z^3 =33

$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =\mathrm{33} \\ $$

Question Number 203807 Answers: 2 Comments: 0

proof : ∫_0 ^1 f^2 (t)dt=0 ⇒ f=0

$$\mathrm{proof}\::\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}^{\mathrm{2}} \left(\mathrm{t}\right)\mathrm{dt}=\mathrm{0}\:\Rightarrow\:\mathrm{f}=\mathrm{0} \\ $$

Question Number 203803 Answers: 1 Comments: 0

Question Number 203800 Answers: 1 Comments: 0

Question Number 203788 Answers: 1 Comments: 0

The sum of all possible products taken two at a time out of the numbers ±1, ±2, ±3, ±4 is (a) 0 (b) −30 (c) 30 (d) 55

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{products}\:\mathrm{taken}\:\mathrm{two}\:\mathrm{at}\: \\ $$$$\mathrm{a}\:\mathrm{time}\:\:\mathrm{out}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\pm\mathrm{1},\:\pm\mathrm{2},\:\pm\mathrm{3},\:\pm\mathrm{4}\:\mathrm{is} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:−\mathrm{30}\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:\mathrm{30}\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\:\mathrm{55} \\ $$

Question Number 203774 Answers: 2 Comments: 0

determine whether the series is convergent or divergent 𝚺_(n=1) ^∞ (n/( (√(4n^2 +1))))

$$\boldsymbol{{determine}}\:\boldsymbol{{whether}}\:\boldsymbol{{the}}\:\boldsymbol{{series}}\:\boldsymbol{{is}} \\ $$$$\boldsymbol{{convergent}}\:\boldsymbol{{or}}\:\boldsymbol{{divergent}} \\ $$$$\underset{\boldsymbol{{n}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\boldsymbol{{n}}}{\:\sqrt{\mathrm{4}\boldsymbol{{n}}^{\mathrm{2}} +\mathrm{1}}} \\ $$

Question Number 203772 Answers: 2 Comments: 0

Question Number 203771 Answers: 1 Comments: 0

Question Number 203782 Answers: 1 Comments: 3

Does a circle have side?

$${Does}\:{a}\:{circle}\:{have}\:{side}? \\ $$$$ \\ $$

Question Number 203750 Answers: 1 Comments: 0

Question Number 203747 Answers: 2 Comments: 0

Question Number 203742 Answers: 3 Comments: 0

Question Number 203736 Answers: 0 Comments: 2

A conductor of length 500cm carried a current of 0.95A when kept in a magnetic field of magnetic flux density 0.5T. Calculate the maximum force acting on it.

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