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  1. u = sqrt(7) * sin(t) du = sqrt(7) * cos(t) * dt du / (u * sqrt(7 - u^2)) => sqrt(7) * cos(t) * dt / (sqrt(7) * sin(t...sqrt(7)) * (ln|sin(t)| - ln|1 + sqrt(1 - sin(t)^2)| + C u = sqrt(7) * sin(t) u / sqrt(7) = sin(t) (1/sqrt(7)) * (ln|u...

    3 Answers · Science & Mathematics · 01/05/2013

  2. u(x) = s(x)/t(x) then u'(x) = [s'(x)t(x) - s(x)t'(x)] / t(x)^2 u''(x...t(x)^2 - [s'(x)t(x) - s(x)t'(x)](2)t(x)t'(x)}/t(x)^4 u''(x) = {[s''(x)t(x)-s(x)t''(x)]t(x)^2 - [s'...

    2 Answers · Science & Mathematics · 24/10/2012

  3. u=√(4-x) u² = 4-x x = 4-u² dx = -2u du So subbing... of your original integral, you now have: ∫(4-u²)(u)(-2u du) = -2 ∫4u² - u^4) du = -2 (4u³/3 - u^5/5) + C...

    3 Answers · Science & Mathematics · 25/06/2009

  4. ∫ dx / x sqrt(x+4) u^2 = x+4 2udu = dx ∫ dx / x sqrt(x+4) = ∫ 2u du / (u^2-4)u = ∫ 2 du / (u^2-4) = 2 ∫ du/(u+2)(u-2) 1/(u+2)(u-2) = A/(u+2) + B/(u-2) 1 = A(u-2) + B(u+2) equate the...

    2 Answers · Science & Mathematics · 06/08/2010

  5. u = 8i + 7j → tan(u) = 7/8 v = 7i - j → tan(v) = - 1/7 tan(a - b) = sin(a - b) / cos(a - b...tan(b)] / [1 + tan(a).tan(b)] → adapt this result to your case tan(u - v) = [tan(u) - tan(v)] / [1 + tan(u).tan(v)] tan(u - v) = [(7/8) - (- 1/7...

    2 Answers · Science & Mathematics · 29/04/2019

  6. A U B = { n ∈ N : 3 or 5 divides n } (A U B...not divide n } B^c = { n ∈ N : 5 does not divide n } A^c U B^c = { n ∈ N : either 3 or 5 does not divide n } So the...

    2 Answers · Science & Mathematics · 03/06/2012

  7. Let u = 1 + 3x^3 Then du/dx = 9x^2............(simple differentiation) So du = 9x...gt; dx = du/9x^2................(divide both sides by 9x^2) Substitute u = 1 + 3x^3 and dx = du/9x^2 to obtain ∫[2 to 4] x^2 (1+3x^3)^2 dx = ∫[2 to 4...

    2 Answers · Science & Mathematics · 16/10/2016

  8. sin(u) = 4/5 = y/z x^2 + y^2 = z^2 x^2 + 4...x^2 = 25 - 16 x^2 = 9 x = 3 1) cos(u) = x/z = 3/5 <==== positive since... to take the positive root. sin(u/2) = + √( (1-cos u)/2 ) sin(u/2) = √( (1- (3...

    3 Answers · Science & Mathematics · 17/08/2011

  9. sec [ arctan(u) + arccos(v)] let arctan(u) = A tan A = u ==> opposite side = u and adjacent side = 1, hypotenuse = √(u^2 + 1) sin A = u / √(u^2 + 1) ------(1) and cos A = 1 / √(u^2 + 1...

    1 Answers · Science & Mathematics · 27/07/2010

  10. If u and v are linearly independent, then whenever c1 u + c2 v = 0 (a zero vector), then c1 = c2 = 0 (as scalars). Also note that span(u, v) for example equals the set of all {c1 u + c2 v} where c1 and c2 range over...

    1 Answers · Science & Mathematics · 22/03/2012

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