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calc 2640

X-intercept? y=0
Y-intercept? x=0
Vertical Asymptote? the limit as X approaches X sub zero of the function = + or - infinity
Horizontal Asymptote? the limit as X approaches + or - infinity of the function = L, graph levels off at y=L at ends.
Oblique Asymptote? is degree of numerator exceeds the degree of the denominator by one. divide numerator by the denominator.
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.
Newton's Method Xn+1 = Xn - (f(Xn)/fprime(Xn))
For area, find delta x... delta x = b-a/n
inscribed means... Under the curve, underestimation
Circumscribed means... over the curve, overestimation
Redefine an index for a summation. (top-bottom)+1
summation of K from K=1 to n n(n+1)/2
summation of K^2 from K=1 to n n(n+1)(2n+1)/6
summation of K^3 from K=1 to n (n(n+1)/2)^2
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)
Riemann sum Approx. Area = summation of f(Xk*)(delta Xk)from K=1 to n
Created by: burtond