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Question Number 84709    Answers: 1   Comments: 0

∫((tan(x)))^(1/3) dx

$$\int\sqrt[{\mathrm{3}}]{{tan}\left({x}\right)}\:{dx} \\ $$

Question Number 84708    Answers: 1   Comments: 0

Question Number 84693    Answers: 1   Comments: 1

Question Number 84689    Answers: 1   Comments: 2

Question Number 84685    Answers: 0   Comments: 0

∫(dx/(x(2−e^x )))

$$\int\frac{{dx}}{{x}\left(\mathrm{2}−{e}^{{x}} \right)} \\ $$

Question Number 84683    Answers: 1   Comments: 0

x∈N and y∈N:(x<y) slove (E): xy−4y+3x−2027=0.....(E)

$${x}\in{N}\:{and}\:{y}\in{N}:\left({x}<{y}\right) \\ $$$${slove}\:\left({E}\right): \\ $$$${xy}−\mathrm{4}{y}+\mathrm{3}{x}−\mathrm{2027}=\mathrm{0}.....\left({E}\right) \\ $$

Question Number 84682    Answers: 0   Comments: 5

Question Number 84681    Answers: 1   Comments: 1

Question Number 84680    Answers: 1   Comments: 0

show that ∫_0 ^1 ∫_0 ^1 ∫_0 ^1 ((log(xyz))/((1+x^2 )(1+y^2 )(1+z^2 ))) dx dy dz=((−3π^2 G)/(16))

$${show}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left({xyz}\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{y}^{\mathrm{2}} \right)\left(\mathrm{1}+{z}^{\mathrm{2}} \right)}\:{dx}\:{dy}\:{dz}=\frac{−\mathrm{3}\pi^{\mathrm{2}} {G}}{\mathrm{16}} \\ $$

Question Number 84677    Answers: 0   Comments: 1

Σ_(k = 1) ^∞ (k^2 /2^k ) ?

$$\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{k}} }\:?\: \\ $$

Question Number 84667    Answers: 0   Comments: 1

Question Number 84666    Answers: 1   Comments: 2

∫ x sin^(−1) (x) dx

$$\int\:{x}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)\:{dx}\: \\ $$

Question Number 84674    Answers: 0   Comments: 1

((6−log_(16) (x^4 ))/(3+2log_(16) (x^2 ))) < 2

$$\frac{\mathrm{6}−\mathrm{log}_{\mathrm{16}} \:\left(\mathrm{x}^{\mathrm{4}} \right)}{\mathrm{3}+\mathrm{2log}_{\mathrm{16}} \left(\mathrm{x}^{\mathrm{2}} \right)}\:<\:\mathrm{2} \\ $$

Question Number 84655    Answers: 2   Comments: 1

Question Number 84651    Answers: 1   Comments: 0

A person stands in the diagonal produced of the square base of a church tower, at a distance 2a from it, and observes the angle of elevation of each of the two outer corners of the top of the tower to be 30°, while that of the nearest corner is 45°. Find the breadth of the tower.

$${A}\:{person}\:{stands}\:{in}\:{the}\:{diagonal} \\ $$$${produced}\:{of}\:{the}\:{square}\:{base}\:{of}\:{a} \\ $$$${church}\:{tower},\:{at}\:{a}\:{distance}\:\mathrm{2}{a} \\ $$$${from}\:{it},\:{and}\:{observes}\:{the}\:{angle} \\ $$$${of}\:{elevation}\:{of}\:{each}\:{of}\:{the}\:{two} \\ $$$${outer}\:{corners}\:{of}\:{the}\:{top}\:{of}\:{the} \\ $$$${tower}\:{to}\:{be}\:\mathrm{30}°,\:{while}\:{that}\:{of}\:{the} \\ $$$${nearest}\:{corner}\:{is}\:\mathrm{45}°.\:{Find}\:{the} \\ $$$${breadth}\:{of}\:{the}\:{tower}. \\ $$

Question Number 84641    Answers: 1   Comments: 1

Question Number 84637    Answers: 0   Comments: 5

prove that lim_(x→∞) (1 + (1/x))^x =e

$$\mathrm{prove}\:\mathrm{that}\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{1}}{{x}}\right)^{{x}} \:={e} \\ $$

Question Number 84632    Answers: 0   Comments: 0

Question Number 84628    Answers: 1   Comments: 1

Question Number 84627    Answers: 1   Comments: 2

1)∣sec(x)∣<2tan(x) on[0,2π] 2)find the cirtical points and the range of f(x)=∣x−3∣+∣2x+1∣

$$\left.\mathrm{1}\right)\mid{sec}\left({x}\right)\mid<\mathrm{2}{tan}\left({x}\right)\:{on}\left[\mathrm{0},\mathrm{2}\pi\right] \\ $$$$ \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{cirtical}\:{points}\:{and}\:{the}\:{range}\:{of} \\ $$$${f}\left({x}\right)=\mid{x}−\mathrm{3}\mid+\mid\mathrm{2}{x}+\mathrm{1}\mid \\ $$$$ \\ $$

Question Number 84624    Answers: 1   Comments: 0

find grad r^m where r=x^2 +y^2 +z^2

$$\mathrm{find}\:\mathrm{grad}\:\mathrm{r}^{\mathrm{m}} \:\:\mathrm{where}\:\mathrm{r}=\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \\ $$

Question Number 84607    Answers: 3   Comments: 1

1)∫(√(sin(x))) dx 2)∫cos(x^2 )dx

$$\left.\mathrm{1}\right)\int\sqrt{{sin}\left({x}\right)}\:{dx} \\ $$$$\left.\mathrm{2}\right)\int{cos}\left({x}^{\mathrm{2}} \right){dx} \\ $$$$ \\ $$

Question Number 84600    Answers: 0   Comments: 9

lim_(x→∞ ) x(√((x−1)/(9x+2))) − (x/3)

$$\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\:{x}\sqrt{\frac{{x}−\mathrm{1}}{\mathrm{9}{x}+\mathrm{2}}}\:−\:\frac{{x}}{\mathrm{3}} \\ $$

Question Number 84588    Answers: 2   Comments: 0

if x − (1/x) = 9 x^3 −(1/x^3 ) = ?

$$\mathrm{if}\:\mathrm{x}\:−\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{9} \\ $$$$\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:? \\ $$

Question Number 84582    Answers: 0   Comments: 10

Question Number 84581    Answers: 0   Comments: 2

let f(x) = e^(2x) ln(1−3x^2 ) 1) calculate f^((0)) (x) and f^((n)) (0) 2) drvelopp f at integr serie 3) find ∫ f(x)dx

$${let}\:{f}\left({x}\right)\:=\:{e}^{\mathrm{2}{x}} {ln}\left(\mathrm{1}−\mathrm{3}{x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left(\mathrm{0}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{drvelopp}\:{f}\:{at}\:{integr}\:{serie} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\int\:{f}\left({x}\right){dx} \\ $$

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