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A midterm exam for math 165, with problems related to limits, derivatives, and tangent lines. Students are required to evaluate limits, find derivatives using the definition, and write the equation of tangent lines. Some problems involve calculus and trigonometry. The exam covers the period from october 2004 to october 2005.
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Midterm Exam Math 165 October 6, 2005 Name:
Show all of your work! If your work is not shown, you will not receive full credit for the problem, even if you have the correct answer.
Section 1: “Pencil and Paper” Problems You have thirty minutes to work on this section. Calculators are not allowed. You do not need to simplify your answers.
In Problems 1 - 4, evaluate the limits (5 points each).
x^2 − 6 x + 9 x^2 − 9
6 x^2 + 9 4 x^3 + 9
sin
4 x
4 x
sin 3θ tan 2θ
In Problems 5 - 10, find dydx. Do not simplify your answers.
sin x x
x^3
x^5
x sin x
x + 1 x^2 + 1
