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Question Number 168909 Answers: 0 Comments: 1

Resolve (1−x^2 y)dx+(x^2 y−x^3 )dy=0 ; μ=μ(x)

$${Resolve}\: \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} {y}\right){dx}+\left({x}^{\mathrm{2}} {y}−{x}^{\mathrm{3}} \right){dy}=\mathrm{0}\:;\:\mu=\mu\left({x}\right) \\ $$

Question Number 168906 Answers: 1 Comments: 0

Question Number 168905 Answers: 1 Comments: 0

Question Number 168898 Answers: 1 Comments: 0

Question Number 168894 Answers: 1 Comments: 1

Question Number 168885 Answers: 0 Comments: 11

Find all the values of n such that: determinant (((digit-sum(n^3 )=n ))) and show that n has at most 2 digits. ^■ digit-sum(abc..^(−) )=a+b+c+...

$$ \\ $$$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that}: \\ $$$$\:\:\:\:\begin{array}{|c|}{\mathrm{digit}-\mathrm{sum}\left(\mathrm{n}^{\mathrm{3}} \right)=\mathrm{n}\:}\\\hline\end{array} \\ $$$$\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{n}\:\mathrm{has}\:\mathrm{at}\:\mathrm{most}\:\mathrm{2}\:\mathrm{digits}. \\ $$$$\:\:^{\blacksquare} \mathrm{digit}-\mathrm{sum}\left(\overline {\mathrm{abc}..}\right)=\mathrm{a}+\mathrm{b}+\mathrm{c}+... \\ $$

Question Number 168881 Answers: 1 Comments: 0

sin(π(√(ix))) + sinh(π(√(ix))) = 0 Find all the real value/s of x.

$$\:\mathrm{sin}\left(\pi\sqrt{\mathrm{ix}}\right)\:+\:\mathrm{sinh}\left(\pi\sqrt{\mathrm{ix}}\right)\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\:\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{real}\:\mathrm{value}/\mathrm{s}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 168878 Answers: 1 Comments: 3

solve: x^(2019) +x^(2020) +x^(2021) +x^(2022) =4

$${solve}:\:\:{x}^{\mathrm{2019}} +{x}^{\mathrm{2020}} +{x}^{\mathrm{2021}} +{x}^{\mathrm{2022}} =\mathrm{4} \\ $$

Question Number 168874 Answers: 0 Comments: 0

Question Number 168873 Answers: 0 Comments: 0

Question Number 168872 Answers: 0 Comments: 2

E=∫^π _0 [((a^2 σ sin θ)/(2ε(√(a^2 −x^2 −2ax cosθ))))]dθ If a>x show that E = ((a^2 σ)/(εx))

$${E}=\underset{\mathrm{0}} {\int}^{\pi} \left[\frac{{a}^{\mathrm{2}} \sigma\:\mathrm{sin}\:\theta}{\mathrm{2}\epsilon\sqrt{{a}^{\mathrm{2}} −{x}^{\mathrm{2}} −\mathrm{2}{ax}\:\mathrm{cos}\theta}}\right]{d}\theta \\ $$$$\mathrm{If}\:{a}>{x}\:\mathrm{show}\:\mathrm{that}\:{E}\:=\:\frac{{a}^{\mathrm{2}} \sigma}{\epsilon{x}} \\ $$

Question Number 168860 Answers: 0 Comments: 0

Question Number 168859 Answers: 1 Comments: 0

Prove that: 1. A + B^(−) = A^(−) ∙ B^(−) , AB^(−) = A^(−) + B^(−) 2. (A + C)(B + C) = AB + C

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{1}.\:\overline {\mathrm{A}\:+\:\mathrm{B}}\:=\:\overline {\mathrm{A}}\:\centerdot\:\overline {\mathrm{B}}\:\:\:,\:\:\:\overline {\mathrm{AB}}\:=\:\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}} \\ $$$$\mathrm{2}.\:\left(\mathrm{A}\:+\:\mathrm{C}\right)\left(\mathrm{B}\:+\:\mathrm{C}\right)\:=\:\mathrm{AB}\:+\:\mathrm{C} \\ $$

Question Number 168858 Answers: 1 Comments: 0

Simplify: 1. (A + B)(A + B^(−) ) 2. (A^(−) + B)(A^(−) + B^(−) )

$$\mathrm{Simplify}: \\ $$$$\mathrm{1}.\:\left(\mathrm{A}\:+\:\mathrm{B}\right)\left(\mathrm{A}\:+\:\overline {\mathrm{B}}\right) \\ $$$$\mathrm{2}.\:\left(\overline {\mathrm{A}}\:+\:\mathrm{B}\right)\left(\overline {\mathrm{A}}\:+\:\overline {\mathrm{B}}\right) \\ $$

Question Number 168857 Answers: 3 Comments: 0

Question Number 168856 Answers: 1 Comments: 0

Re(2+e^(iαt) )?

$$\mathrm{Re}\left(\mathrm{2}+\mathrm{e}^{\mathrm{i}\alpha\mathrm{t}} \right)? \\ $$

Question Number 168855 Answers: 0 Comments: 0

Question Number 168852 Answers: 0 Comments: 3

Question Number 168868 Answers: 0 Comments: 0

Question Number 168842 Answers: 0 Comments: 0

Question Number 168841 Answers: 0 Comments: 0

Question Number 168832 Answers: 1 Comments: 1

Question Number 168830 Answers: 0 Comments: 1

Question Number 168828 Answers: 0 Comments: 1

∫_0 ^(π/2) cos^(−1) ((1/(1+2cos x)))dx

$$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2cos}\:{x}}\right){dx} \\ $$

Question Number 168821 Answers: 1 Comments: 0

lim_(x→a) ((a^x −a^n )/(nln(x)−nln(a)))=?

$$\underset{{x}\rightarrow{a}} {\mathrm{lim}}\frac{{a}^{{x}} −{a}^{{n}} }{{nln}\left({x}\right)−{nln}\left({a}\right)}=? \\ $$

Question Number 168819 Answers: 3 Comments: 0

De^ montrer que: Demonstrate that: lim_(x→0) (((e^x −1−ln (x+1))/(cos (x)−1))) = −2

$$\mathrm{D}\acute {\mathrm{e}montrer}\:\mathrm{que}: \\ $$$$\mathrm{Demonstrate}\:\mathrm{that}: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{{e}^{{x}} −\mathrm{1}−\mathrm{ln}\:\left({x}+\mathrm{1}\right)}{\mathrm{cos}\:\left({x}\right)−\mathrm{1}}\right)\:=\:−\mathrm{2} \\ $$

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