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  1. b) Your series is essentially a geometric series. So use the formula 1 + z + z^2 + ...+ z^n + ...= 1/(1-z) when | z | < 1. Begin by rewriting the series to get it into desired form: x^3/8 + x^5/64 + ...+ x^(2n+1)/8^n + ..... ....= x^3/8{1 + x^2/8 + ...+ (x^2/8)^(n-1...

    1 Answers · Science & Mathematics · 29/06/2014

  2. It's a progression from the first two courses. If you aced Calculus I and II, you should have no trouble with III as long as you put in the same level of work.

    2 Answers · Science & Mathematics · 13/07/2014

  3. There's 13 hearts. There's 3 aces that aren't hearts. So, there's 16 favorable cards, in a set of 52 cards. The chance of drawing them are 16/52 = 4/13

    1 Answers · Science & Mathematics · 07/04/2014

  4. ...7,8,9,10,J,K,Q,A (8 cards: assuming ace is higher than 6). There are 4 suites. 8x4...

    2 Answers · Science & Mathematics · 08/04/2014

  5. ... y/2 = 1/x => y = 2/x Pythagoras' formula on Δ ACE: L² = (x+1)² + (2/x+ 2)² derive (L²)' = 2(x+1...

    1 Answers · Science & Mathematics · 29/03/2014

  6. The probability is the same. All that matters is that you are dealt two cards, and you have zero information about the other 50. If you're alone you get cards 1 and 2. But the probability is the same for all...

    1 Answers · Science & Mathematics · 21/01/2014

  7. The odds are the same no matter how many opponents there are. The deck does not know or care what you do with the other 50 cards . .

    1 Answers · Science & Mathematics · 21/01/2014

  8. ... will be fine. You can ask teacher or anyone for help. You can ace it. You can do all things through Jesus Christ who...

    4 Answers · Science & Mathematics · 23/12/2013

  9. 2) Let u = (r, s) where r and s are both not 0. So, D_αu f(a, b) = lim(h→0) [f(a + αrh, b + αsh) - f(a, b)] / (h ||αu||) = lim(h→0) [f(a + αrh, b + αsh) - f(a, b)] / (αh ||u||), since α > 0 = lim(k→0) [f(a + rk, b + sk) - f(a, b)] / (k ||u||), letting k = αh = lim(k→0) [f(a + rk, b + sk) - f(a, b...

    1 Answers · Science & Mathematics · 12/12/2013

  10. The second should be easy because the directional derivative ONLY involves a direction, NOT an amplitude. By multiplying by a scalar you only change the magnitude, not the direction (unless α is negative in which case you just negate the directional derivative--but we don't...

    1 Answers · Science & Mathematics · 12/12/2013

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