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UCSD MATH 10C - Midterm 1 Review

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Midterm 1 ReviewMary RadcliffeMath 10CFall 2010October 15, 2010Chapter 8IKnow the definition of pdf (p(x)) and cdf (P(x)), that is,P(b)−P(a) = proportion of values between a and b =Zbap(x)dx.IKnow how to use p and P to calculate probabilities.IKnow how to get p from P and vice versa: p(x) = P0(x) andP(x) =Rx−∞p(t)dt.IKnow how to calculate mean: mean=R∞−∞xp(x)dx.IKnow how to calculate median: If T is the median, thenRT−∞p(x)dx =12, that is, P(T ) =12.IBe able to interpret pdfs and cdfs in terms of the distributionsthey represent.Chapter 9IKnow what a geometric series is: a1+ a2+ a3+ · · · isgeometric if the nth term is of the form an= a1rn−1.IKnow how to calculate sums of finite geometric series: ifSn= a1+ a1r + a1r2+ · · · + a1rn−1, then Sn= a1rn−1r −1.IKnow how to calculate sums of finite geometric series: IfS = a1+ a1r + a1r2+ · · · is an infinite sum, thenIIf |r | < 1, then S = a111−r.IIf |r | ≥ 1 then S is either infinite (when r is positive) orundetermined (when r is negative).Chapter 10IIf f (x) is a function, know how to calculate the nth Taylorapproximation Pn(x) to f near a point a:Pn(x) = C0+ C1(x − 1) + C2(x − a)2+ · · · + Cn(x − a)n,where Cn=f(n)(a)n!.IUnderstand how to use the Taylor polynomial to approximatethe function (that is, f (x) ≈ Pn(x) for x near a).Chapter 12IUnderstand how to interpret graphs in 3-space, the x − y − zaxis system, and how to plot points in 3-space.IBe able to calculate the distance d between two points: Thedistance between (x1, y1, z1) and (x2, y2, z2) is given byd =q(x1− x2)2+ (y1− y2)2+ (z1− z2)2.IBe able to find the equation of a sphere in 3-space: Thesphere with radius r centered at (x0, y0, z0) is given by theequationr2= (x − x0)2+ (y − y0)2+ (z − z0)2.Chapter 12IUnderstand how to interpret a table of values for a functionf (x, y).IBe able to calculate cross-sections of z = f (x, y) with x or yfixed, and use them to sketch a graph of the function.IBe familiar with some basic functions of two variables, such asIz = f (x, y) = x2+ y2Iz = f (x, y) = x2− y2IShifts and stretches of the above two functions (likez = f (x, y) = (2x)2+ (y − 1)2)IKnow what a cylinder is (a function in 3-space where only twovariables appear in the expression, such as z = x2) and beable to graph cylindrical functions.Chapter 12IBe able to draw a contour diagram for a function z = f (x, y)and use it to interpret the function.IKnow how to sketch the graph of a function using theinformation in the contour diagram.Chapter 12IKnow the equation of a plane: either z = c + mx + ny, orz = z0+ m(x − x0) + n(y − y0), where m is the slope in thex-direction, n is the slope in the y -direction, and (x0, y0, z0) isa point on the plane.IBe able to calculate the equation of a plane given three(non-colinear) points on the plane.IUnderstand what the contour diagram for a plane looks like;be able to explain it both in words and with a sketch.IBe able to fill in the table of values for a linear function. Beable to use the table of values for a linear function tocalculate the slope in both the x and y


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UCSD MATH 10C - Midterm 1 Review

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