10121FinalExamReview

10121FinalExamReview - MTH 121 FINAL EXAM REVIEW The final...

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Unformatted text preview: MTH 121 FINAL EXAM REVIEW The final exam will be given on Apr 26 (in class). It will be cumulative. However, there will be an emphasis on the material covered since Test 2, i.e., Sec 4.5-6, Chapter 5/6. You can refer to Test 1 review and Test 2 review for Chapter 0-4 material. For your convenience, I put them together here. Chapter 0 Functions • Sec 0.1 Functions and their graphs: domain of a function. • Sec 0.2 Some important functions: Linear function and quadratic functions, polyno- mials and rational functions; absolute value and piecewisely dened functions. • Sec 0.3 Algebra of functions: Arithmetic and composition of functions. • Sec 0.4 Zeros of functions: Use quadratic formula to solve equations and factor polyno- mials. • Sec 0.5 Exponents and power functions: – Radicals and exponents: n √ x m = x m n – Exponent laws: x r x s = x r + s , ( x r ) s = x rs , ( xy ) r = x r y r , x r x s = x r- s , 1 x r = x- r , ( x y ) r = x r y r . Chapter 1 The Derivative Sec 1.1 Straight lines: • Slope-intercept equation: y = mx + b . • Point-slope equation: y- y 1 = m ( x- x 1 ). • Two point equation: y- y 1 = y 2- y 1 x 2- x 1 ( x- x 1 ). • Two lines are parallel if they have the same slope: m 1 = m 2 . • Two lines are perpendicular if their slopes are negative reciprocals of each other: m 1 · m 2 =- 1. Sec 1.2,1.3,1.6,1.7 Derivative rules: should be able to apply the following rules to compute the derivative or second derivative: • (constant rule): d dx ( k ) = 0 • (constant-multiple rule): d dx ( kf ( x )) = k d dx ( f ( x )) • (power rule): d dx ( x r ) = rx r- 1 • (sum rule): d dx ( f ( x ) ± g ( x )) = d dx ( f ( x )) ± d dx ( g ( x )) • (generalized power rule) d dx ( g ( x )) r = rg ( x ) r- 1 d dx ( g ( x )) • (2nd derivative) d 2 dx 2 ( f ( x )) = d dx ( d dx ( f ( x ))) • Notations: f ( x ) = d dx ( f ( x )); f ( x ) = d dx ( d dx ( f ( x ))) Sec 1.4 Limits and the derivative: • understand the definition of limit. • know how to compute a limit....
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10121FinalExamReview - MTH 121 FINAL EXAM REVIEW The final...

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