# UMass Amherst MATH 127 - final practice calc (25 pages)

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## final practice calc

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- Pages:
- 25
- School:
- University of Massachusetts Amherst
- Course:
- Math 127 - Calculus for the Life and Social Sciences I

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Calculus I Review Problems 1 New York University Exam is on Sections 2 3 2 6 2 8 3 1 3 5 3 7 4 1 4 2 4 3 4 4 4 5 4 7 5 1 5 5 1 Compute the following limits a limx 3 e2 x 3 Solution 1 1 1 b limx 10 ln 100 x2 Solution c limx e x sin x Solution d 1 2x limx 1 2 x Solution You can also apply L Hospital s e limx x3 e x Solution x f limx 1 x 1 1 Solution Page 1 Page 1 Page 1 1 ln x g limx 2 tan xcos x Solution h lim x ln x 5 ln x Solution lim x ln x 5 x lim x 5 x ln 1 x lim 5 x2 x 5 x x12 lim 5x x2 x 5 1 x2 lim 5x x 5 5 2 Calculate y 0 a y 2x x2 1 0 1Solution y 1 b y sin x sin x 1 Solution 2 x2 1 2x2 x2 1 1 2 x2 1 sec 2 c y 1 tan 2 1Solution 1 d xy 4 x2 y x 3y Solution Page 2 e sin xy x2 y Solution f y ln x2 ex Solution g y cos x x Solution 1 1 h y ln 1 x 1 Solution Page 1 1 ln x 1 i y arctan arcsin x 1 Solution j xey y 1 Solution k y tan x 1 x Solution 2 l ex y x y Solution Page Page12 3 The graph of y x3 9x2 16x 1 has a slope of 5 at two points Find the coordinates of the points Solution y0 5 0 3x2 18x 16 3x2 18x 16 0 0 x 3x2 18x 21 x2 6x 7 x 1 x 7 1 or x 7 When x 1 y 7 when x 7 y 209 Thus the two points are 1 7 and 7 209 4 Find the equation of the line tangent to f x at x 2 if f x x3 4 2 3x Solution The slope of the tangent line is the value of the first derivative at x 2 Differentiating gives d x3 4 d 1 3 4 1 x x dx 2 3x dx 2 3 1 4 3x2 1 x 2 2 3 3 2 4 x 2 2 3x For x 2 f 0 2 3 2 4 1 2 6 6 333 2 3 2 2 3 and f 2 23 4 2 4 3 333 2 3 2 3 To find the y intercept for the tangent line equation at the point 2 3 333 we substitute in the general equation y b mx and solve for b 3 333 9 333 b 6 333 2 b The tangent line has the equation y 9 333 6 333x 5 a Find the slope of the graph of f x 1

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