calc 2640
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| X-intercept? | y=0
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| Y-intercept? | x=0
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| Vertical Asymptote? | the limit as X approaches X sub zero of the function = + or - infinity
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| Horizontal Asymptote? | the limit as X approaches + or - infinity of the function = L, graph levels off at y=L at ends.
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| Oblique Asymptote? | is degree of numerator exceeds the degree of the denominator by one. divide numerator by the denominator.
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| Cusp? | If: 1) f(x) is continuous at Xsubzero
2) f(x) has a vertical tangent at x=xsubzero 3) fprime(x)goes to infinity on one side and -infinity on the other.
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| Newton's Method | Xn+1 = Xn - (f(Xn)/fprime(Xn))
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| For area, find delta x... | delta x = b-a/n
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| inscribed means... | Under the curve, underestimation
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| Circumscribed means... | over the curve, overestimation
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| Redefine an index for a summation. | (top-bottom)+1
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| summation of K from K=1 to n | n(n+1)/2
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| summation of K^2 from K=1 to n | n(n+1)(2n+1)/6
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| summation of K^3 from K=1 to n | (n(n+1)/2)^2
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| steps to interpret an antiderivative as area | 1) delta x
2) points of subdivision
3) area of Kth rectangle(Ak = f(Ck)(delta x)
4)approimate total area(summation from K=1 to n)
5)Actual area (limit of approx. area)
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| Riemann sum | Approx. Area = summation of f(Xk*)(delta Xk)from K=1 to n
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Created by:
burtond
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