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Question Number 169897    Answers: 0   Comments: 1

Question Number 169896    Answers: 1   Comments: 0

Question Number 169892    Answers: 1   Comments: 0

(dy/dx) = 2xe^(−y) , y(1) = 0

$$\frac{{dy}}{{dx}}\:=\:\mathrm{2}{xe}^{−{y}} \:,\:\:{y}\left(\mathrm{1}\right)\:=\:\mathrm{0} \\ $$

Question Number 169885    Answers: 1   Comments: 0

∣a^→ ∣=13 ∣b^→ ∣=19 ∣a^→ +b^→ ∣=24 ∣a^→ −b^→ ∣=?

$$\mid\overset{\rightarrow} {{a}}\mid=\mathrm{13} \\ $$$$\mid\overset{\rightarrow} {{b}}\mid=\mathrm{19} \\ $$$$\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid=\mathrm{24} \\ $$$$\mid\overset{\rightarrow} {{a}}−\overset{\rightarrow} {{b}}\mid=? \\ $$

Question Number 169878    Answers: 2   Comments: 0

Question Number 169874    Answers: 1   Comments: 0

Σ_(d∣6) d=?

$$\underset{{d}\mid\mathrm{6}} {\sum}{d}=? \\ $$

Question Number 169873    Answers: 2   Comments: 0

∫_0 ^1 ((ln(1+x))/x)dx=?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx}=? \\ $$

Question Number 169870    Answers: 0   Comments: 0

In an artistic design by a contractor of the students’ centre in a university, four pillars were erected to form two triangular figures with the vertices at the first floor of the building and two of the pillars crossing each other. Proof that the spaces occupied by these two triangular figures are equal.

$$ \\ $$In an artistic design by a contractor of the students’ centre in a university, four pillars were erected to form two triangular figures with the vertices at the first floor of the building and two of the pillars crossing each other. Proof that the spaces occupied by these two triangular figures are equal.

Question Number 169865    Answers: 3   Comments: 2

x+y=−2 xy=4 find x^8 +8y^5 =?

$${x}+{y}=−\mathrm{2} \\ $$$${xy}=\mathrm{4} \\ $$$${find}\:{x}^{\mathrm{8}} +\mathrm{8}{y}^{\mathrm{5}} =? \\ $$

Question Number 169864    Answers: 1   Comments: 0

Question Number 169863    Answers: 1   Comments: 0

∫_o ^1 xln∣x^2 −2x∣dx

$$\int_{{o}} ^{\mathrm{1}} {xln}\mid{x}^{\mathrm{2}} −\mathrm{2}{x}\mid{dx} \\ $$

Question Number 169860    Answers: 1   Comments: 0

y = x^2 + 1 y = 0 x = - 1 x = 2 find the volume of the object obtained by rotating the figure bounded by lines around the abscissa axis

$$\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1} \\ $$$$\mathrm{y}\:=\:\mathrm{0} \\ $$$$\mathrm{x}\:=\:-\:\mathrm{1} \\ $$$$\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{object}\:\mathrm{obtained} \\ $$$$\mathrm{by}\:\mathrm{rotating}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{bounded}\:\mathrm{by}\:\mathrm{lines} \\ $$$$\mathrm{around}\:\mathrm{the}\:\mathrm{abscissa}\:\mathrm{axis} \\ $$

Question Number 169859    Answers: 0   Comments: 0

Question Number 169855    Answers: 1   Comments: 0

Question Number 169852    Answers: 1   Comments: 0

y = x^2 + 2 y = - x x = 0 x = 1 find the area of the figure bounded by lines

$$\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{2} \\ $$$$\mathrm{y}\:=\:-\:\mathrm{x} \\ $$$$\mathrm{x}\:=\:\mathrm{0} \\ $$$$\mathrm{x}\:=\:\mathrm{1} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{bounded}\:\mathrm{by} \\ $$$$\mathrm{lines} \\ $$

Question Number 169850    Answers: 0   Comments: 1

Question Number 169849    Answers: 1   Comments: 0

Question Number 169842    Answers: 1   Comments: 0

Question Number 169837    Answers: 0   Comments: 0

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Question Number 169836    Answers: 1   Comments: 0

Question Number 169831    Answers: 0   Comments: 0

Question Number 169826    Answers: 1   Comments: 0

Given f(x)=(√(sin x)) +(√(3 cos x)) x∈ (0, (π/2)) Find max f(x).

$$\:\:{Given}\:{f}\left({x}\right)=\sqrt{\mathrm{sin}\:{x}}\:+\sqrt{\mathrm{3}\:\mathrm{cos}\:{x}}\: \\ $$$$\:\:{x}\in\:\left(\mathrm{0},\:\frac{\pi}{\mathrm{2}}\right) \\ $$$$\:{Find}\:{max}\:{f}\left({x}\right).\: \\ $$

Question Number 169825    Answers: 1   Comments: 0

Question Number 169821    Answers: 2   Comments: 0

Question Number 169815    Answers: 1   Comments: 8

Question Number 169812    Answers: 0   Comments: 0

Show that f(z)=z^2 is harmonic in the polar form Mastermind

$${Show}\:{that}\:{f}\left({z}\right)={z}^{\mathrm{2}} \:{is}\:{harmonic}\:{in}\:{the} \\ $$$${polar}\:{form} \\ $$$$ \\ $$$${Mastermind} \\ $$

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