Calculus and Analytic Geo Notes 2012

Calculus and Analytic Geo Notes 2012 - Math 131 Homework 2...

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Math 131 Homework 2 1. The point P (4, 3) lies on the curve . a. If Q is the point , use your calculator to find the slope of the secant line PQ (correct to 6 decimal places) for the following values of x. (i) 3.5 -7.2 (ii) 3.9 4.11 (iii) 3.99 3.76 (iv) 4.5 2.56 (v) 4.1 3.41 (vi) 4.01 3.698 b. Using the results in part (a), guess the value of the slope of the tangent line to the curve at P (4, 3). 3.732050 c. Using the slope in part (b), find an equation of the tangent line to the curve at P (4, 3). Slope tan = 1/(sqrt(4) - sqrt(3)) 2. The point P (0, 0) lies on the curve . a. If Q is the point , use your calculator to find the slope of the secant line PQ (correct to 6 decimal places) for the following values of x. (i) – 0.5 .5 (ii) – 0.1 .1 (iii) – 0.01 .01 (iv) 0.5 .5 (v) 0.1 .1 (vi) 0.01 .01 b. Using the results in part (a), guess the value of the slope of the tangent line to the curve at P (0, 0). 0 c. Using the slope in part (b), find an equation of the tangent line to the curve at P (0, 0).
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Unformatted text preview: Slope tan = x + a 3. The point P lies on the curve . a. If Q is the point , use algebra to guess the value of the slope of the tangent line to the curve at P . Slope tan = -1/(4(x+2)) = -1/16 Note: I edited the y in point Q from 1/x to 1/(x+2) 4. The point P lies on the curve . a. If Q is the point , use algebra to guess the value of the slope of the tangent line to the curve at P . If x = 2.0000001, tan slope = 1/3 5. The point P lies on the curve . a. Use algebra to guess the value of the slope of the tangent line to the curve at P (3, 6). M sec = x+2 = 5 b. Use algebra to guess the value of the slope of the tangent line to the curve at a point (x^2-x-a^2+a)/(x-a) if x=1.0001, slope = 4.999, so slope guess is 5 6. A ball is thrown straight upward. After t seconds, the height is feet. Use algebra to guess the velocity of the ball after 3 seconds. If t =3 then 270 feet...
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