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Coordinate Changing, Equation of Tangent Line, Particle Moves Along Graph, Length of Shadow, Value of Parabola, Numerical Value, Derivative of Function, Implicit Differentiation are some points from this exam paper of Calculus I.
Typology: Exams
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Name: Calculus I; Fall 2007
Part I consists of 6 questions, each worth 5 points. Clearly show your work for each of the problems listed.
(1) Find the equation of the tangent line to the graph of y = 3x^2 + 2x + 5 at x = 1.
(2) If y = x sin(x), find y′.
(3) If y = 3
x^4 + x^2 + 1, find y′.
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(4) If y = x (^2) + x^2 − 1 , find^ y
′. Simplify your answer.
(5) If y = x
(^7) −√ 3 x (^3) +x x , find^ y
′. Simplify your answer.
(6) If y = sin(tan(x^3 + 1)), find y′. [You don’t need to simplify the answer.]
(3) If a flash light is located on the ground 10m from a building and shines a light on a man who is 2m tall and walks towards the building at a speed of. 2 m/s, how fast is the length of his shadow on the wall of the building changing when he is 3m from the building?
(4) Find y′^ if x^2 + y^2 = cos(xy).
(5) Find y′^ if y =
√x (^2) + x^2 − 1. Simplify your answer.
