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Maclaurin series again |
2000-09-23 |
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Jason Rasmussen pose la question : I suppose my confusion comes into play when I am trying to figure out where the xn term comes from. I know that the Power Series notation is directly related to the Geometric Series of the form sigma [ brn ] where the limit is b/(1-r) for convergence at | r | <1. Therefore, the function f(x) needs to somehow take the form of b/(1-(x-a)), which may take some manipulation, and by setting r = (x-a) and b = Cn, we get the Geometric Series converted to the Power Series. Taking the nth order derivative of the Power Series gives Cn = fn(a)/n!. There must be a gap in my knowledge somewhere because I cannot seem to make f(x) = ex take the form of f(x) = b/(1-(x-a)). Maybe I should have labelled my question as "middle" because it may be more of a personal problem with algebra and logarithms. Or, am I to assume that all functions can be represented by sigma [fn(a) * (x-a)n / n!]? Harley Weston lui répond. |
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BEDMAS |
2000-09-22 |
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Monica Zimmer pose la question : In the Math rule BEDMAS does it matter if you do the division or the multiplication first? Penny Nom lui répond. |
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Mode |
2000-09-22 |
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James Barton pose la question : I have always been told that a mode is the "one" number that appears most in the set of numbers: ex.{1,3,4,6,3,2} the mode is 3. What if you have {1,1,3,4,5,5}is there a mode. I was taught long ago that there is no mode, Not i am having to teach there is two modes. 1 and 5. If this is the case if we have {1,1,2,2,3,3,4,4,5,5} that every number is the mode. True or false. This is being ambigiuous if we say all are the mode. Because no one number is used more than the others. Claue Tardif and Harley Weston lui répond. |
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Permutations and Multiplication Principle |
2000-09-22 |
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Candice pose la question : A forester selects 4 pink and 4 white dogwoods. The trees are to be planted in row. If a tree is distinguished by color only, in how many ways can the eight dogwoods be planted? How many of these arrangements have at least two trees of the same color side by side? Denis Hanson and Claude Tardif lui répond. |
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Dividing a region in half |
2000-09-21 |
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Kerry pose la question : There is a line through the origin that divides the region bounded by the parabola y=x-x2 and the x-axis into two regions with equal area. What is the slope of the line? Penny Nom lui répond. |
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A Maclaurin series |
2000-09-21 |
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Jason Rasmussen pose la question : I have a question regarding power series notation for certain functions within the interval of convergence. Harley Weston lui répond. |
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Leap Year |
2000-09-20 |
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Jennifer pose la question : The earth revolves around the sun in 365.24 days. How does our calendar deals with the extra 0.24 day? Penny Nom lui répond. |
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A cycloid in Cartesian form |
2000-09-20 |
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Billy pose la question : The parametric equation of cycloid is given: x=r(t-sint) y=r(1-cost) How to eliminate t? Harley Weston lui répond. |
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Arithmetic in base 5 |
2000-09-20 |
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Lesley Emerson pose la question : my daughter is 9 and has been aske to solve the following in base 5 3+2 4+10 . . . Penny Nom lui répond. |
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A proof that 1=2 |
2000-09-19 |
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sporky pose la question : Why does the proof for 1=2 not work? x = 1 x2 = 1 x = x2 1 = 2x (derivitive) 1 = 2(1) 1 = 2 ??? please tell me where the false logic is. Walter Whiteley lui répond. |
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Order of operations |
2000-09-19 |
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Nicole pose la question : the problem is, 4x8-18 divided by 6= do you solve this by doing 4x8=32 then by dividing 18by 6= 3, then subtracting 3 from 32 = 29? If not what is the order of operation? Penny Nom lui répond. |
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Circular Permutations |
2000-09-18 |
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J. Stuart pose la question : I am able to understand the simple theory behind circular permutations (that is, there are (n-1)! ways to arrange n people in a circle. One question, however, is giving me some difficulty. It reads: In how many ways can four married couples be arranged around a circular table if each man must sit beside his wife? Any suggestions you have would be greatly appreaciated. Penny Nom lui répond. |
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Buying art supplies |
2000-09-18 |
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Travis pose la question : An art teacher buys exactly 100 items at this sale, and the total cost before tax is $100. She buys at least one of each item. How many of each item does she buy? Markers $0.50 Sketch Pads $3.00 Paint Sets $10.00 Denis Hanson lui répond. |
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Probability of a square |
2000-09-18 |
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Nick pose la question : What is the probability that four different points chosen at random from the fifteen equally-spaced points shown are the vertices of a square? I need to have my answer expressed as a common fraction. Help! I don't know how to write it. . . . . . . . . . . . . . . . Penny Nom lui répond. |
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Review problems |
2000-09-18 |
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Dee pose la question : A card is selected from an ordinary deck of cards. What is the probability of. . . selecting 2 aces in a row? If you toss two dice, what would be your probability of the following? . . . Penny Nom lui répond. |
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