MATH 121 Lecture Notes - Quotient Rule, Asymptote, Scilab

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turquoisegnu128

9 Jan 2019

School

University of Maryland

Department

Mathematics

Course

MATH 121

Professor

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Document Summary

1. (a) you are given the following table of values: x f (x) f (x) g(x) g (x) What is the linear approximation to h(3. 02)? (this is also called the di erential or tangent line approximation. ) Solution. h (3) = (g (f (3))f (3) = g (1)f (3) = (2/7)( 8) = 16/7. Let x be the length of a horizontal size and y the length of a vertical side, in feet. The cost c in dollars is then c = 20(2x) + 10(2y). 20y = 160 40x y = 8 2x . A = xy = x(8 2x) = 8x 2x2. Then a (x) = 0 at x = 2. A is maximum at x = 2 because a (x) > 0 for x < 2 and a/(x) < 0 for x > 2. When x = 2, we have y = 8 2x = 4. So, the maximum area xy is 8 square feet.

Related Questions

Problem 4 Circle your answer. a) (6 points) If f(x) = 2x + 3x2 - 361 + 5, then the tangent line to the graph y= f(x) is horizontal when i) 1 = -2,3 ii) I = 2,-3 iii) r = 0 iv) not listed b) [6 points] Suppose Given h(x) = f(g(T)), where g(2) = 3, g'(2) = 7, f'(2) = -1 and 1'(3) = -2. Then h'(2) is equal to i) - 1 ii) -2 iii) - 14 iv) not listed (x+3)(1 - 1)3 c) (6 points) The function f(1) == (x2 - 2x + 1)(x + 3) wa has vertical asymptotes at i) x = -3,0 ii) = -3,0,1 iii) x = 0,1 iv) not listed d) (6 points] The solution to the initial value problem v'(x) = 473 – cos(x) +e", y(0) = 3 is i) y(x) = x + sin(x) + e* + 2 ii) y(I) = x4 – sin(x) +et+2 iii) y(x) = 2* – sin(1) + et + 3 iv) not listed