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Question Number 168964 Answers: 2 Comments: 0

lim_(x→0) ∫_0 ^x ((sin 2t)/( (√(4+t^2 )) ∫_0 ^x ((√(1+t))−1)dt)) dt =?

$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\frac{\mathrm{sin}\:\mathrm{2}{t}}{\:\sqrt{\mathrm{4}+{t}^{\mathrm{2}} }\:\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\left(\sqrt{\mathrm{1}+{t}}−\mathrm{1}\right){dt}}\:{dt}\:=?\: \\ $$

Question Number 168926 Answers: 2 Comments: 2

Question Number 168921 Answers: 1 Comments: 0

Question Number 168911 Answers: 1 Comments: 1

Question Number 168910 Answers: 0 Comments: 3

Resolve 1) (x−y)ydx−x^2 dy=0 2)(2x−y)dx+(4x−2y+3)dy=0

$${Resolve} \\ $$$$\left.\mathrm{1}\right)\:\left({x}−{y}\right){ydx}−{x}^{\mathrm{2}} {dy}=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{2}{x}−{y}\right){dx}+\left(\mathrm{4}{x}−\mathrm{2}{y}+\mathrm{3}\right){dy}=\mathrm{0} \\ $$

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

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