# Review-Final - Review for final exam of Math 201 Jing Zhang...

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Review for final exam of Math 201Jing ZhangNovember 19, 2014Useful formulas and methods1. (1)Distance FormulasThe distance between any two pointsP(x1, y1) andQ(x2, y2) in the coordinate plane, denotedd(P, Q), isd(P, Q) =p(x2-x1)2+ (y2-y1)2(2)Midpoint FormulaThe coordinates of the midpointM(x, y) on the line segment joiningP(x1, y1) andQ(x2, y2)are given byM(x, y) = (x1+x22,y1+y22)2. (1)Slope of a lineThe slope of a nonvertical line that passes through the pointsP(x1, y1) andQ(x2, y2) is denotedbymand is defined bym=y2-y1x2-x1, x16=x2(2)Equations of a line(a) Point-Slope form of the equation of a line:An equation of the line that passes through the point (x1, y1) and has slopemisy-y1=m(x-x1)(b) Slope-Intercept form of the equation of a line:An equation of the line that has slopemandy-interceptbisy=mx+b(c) General equation of a line:Ax+By+C= 0, A, B, Care constants1
3. (1)Parallel Lines:Two nonvertical lines are parallel if and only if they have thesame slope.(2)Perpendicular Lines:Two lines with slopesm1andm2are perpendicular if and only ifm1m2=-1,that is, theirslopes are negative reciprocals:m2=-1m1(3)Finding Equations of Parallel and Perpendicular Lines:Let a linel:Ax+By+C= 0. Find the equation of each line through the point (x1, y1):(a)l1parallel tol;(b)l2perpendicular tol.Step 1 Find the slopemofl.Writelin the formy=mx+b.Step 2 Write slope ofl1andl2.The slopem1ofl1ism.The slopem2ofl2is-1m.Step 3 Write equation ofl1andl2.Use point-slope form to write equations ofl1andl1.Simplify to write equations in the requested form.4.Equation of a circle:(1) Thestandard formfor the equation of a circle with center (h, k) and radiusris(x-h)2+ (y-k)2=r2(2) If you are given the equation of a circle in general form. Then to find its center and radius,you must put the equation back in standard form. To do this, you need to complete the squarefor all thexandy-terms. To makex2+bxa perfect square, add (12b)2to getx2+bx+ (12b)2= (x+12b)25.Rational Functions;(1)x-intercepts: In order to find thex-intercepts, you just sety= 0 and solve forx. Forthe rational function:y= 0 equivalent to the numerator equals to 0.2
y-intercepts: In order to find they-intercepts, you just setx= 0 and solve fory.(2)Vertical asymptotes;There are two steps to find the vertical asymptotes of the rational functions;Step 1:Make sure that the denominator and the numerator do not have common fac-tor;(Cancel the common factor)Step 2:Let the denominator to be equal to zero and solve forx.(3)

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Sin, Inverse function, Inverse trigonometric functions, tan
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