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The october 2005 ma 125 test 2 for a mathematics course. It includes instructions for the exam, 15 math problems to be solved, and a bonus problem. Students are not allowed to use calculators, notes, or books during the exam and must justify their answers mathematically.
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MA 125 Test 2 Oct. 2005. NAME You may not use calculators, notes, or books. Do your own work. On both Part 1 and Part 2: Justify your answers mathematically. ‘Show your work.’ CIRCLE ANSWERS.
PART 1. Little or no partial credit. 5 points each. In 1-9 find the derivative of each of the functions. Use parentheses where needed and simplify your answers (collect like terms and leave no complex frac- tions). (1.) f (x) = 2x^3 + e^5 x
(2.) h(x) = x cos(3x)
(3.) g(z) = z
2 1+z^3
(4.) w(x) = (x^5 + x − 3)^8
(5.) F (z) =
5 + z^4
(9.) Q(x) = 3x
(10.) Use implicit differentiation to find y′, derivative of y if x^2 +xy +y^2 = 4.
PART 2. Partial credit may be given.
(b) Find all times at which the velocity is zero.
(c) Find the acceleration a(t) at time t.
(d) Find all times at which the acceleration is zero.
(b) Find all intervals on which the graph of w is concave up.
x. (a) Find the linearization L(x) of F (x) at x = 9.
(b) Use the linearization of F to approximate
Bonus Problem (6 points) Find all points (x, y) on the curve x^2 + xy + y^2 = 1 such that the tangent line is parallel to the line y = −x + 2.
