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Mth 201 Hour Exam 2: Calculus Problems - Prof. Aaron D. Wootton, Exams of Calculus

A math exam consisting of 9 problems, including short answer and long answer questions. Topics covered include differentiation using various rules, finding derivatives, and using given information to determine speed. Students are required to provide exact answers and explanations for long answer questions.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

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koofers-user-5na 🇺🇸

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Mth 201
Hour Exam 2
Name: Date:
9 Problems. 100 Points. Follow directions carefully. Please
do not leave any question blank, and turn off cell phones and
other noisemakers to avoid disturbing your classmates.
I have verified that this exam contains 9 problems and 6 printed pages.
Initial .
Print the name of the people sitting either side of you :-
Short Answer (7 points each) - Minimal explanation and calcula-
tions necessary though where appropriate, answers should be ex-
act.
1. Differentiate the function f(x) = eπe2
πeπ
2eπ2+sin(π/8) with respect to x.
2. What is the slope of the tangent line to f(x) = x23πx + 2 at x= 0?
1
pf3
pf4
pf5

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Mth 201 Hour Exam 2

Name: Date:

9 Problems. 100 Points. Follow directions carefully. Please do not leave any question blank, and turn off cell phones and other noisemakers to avoid disturbing your classmates.

I have verified that this exam contains 9 problems and 6 printed pages. Initial.

Print the name of the people sitting either side of you :-

Short Answer (7 points each) - Minimal explanation and calcula- tions necessary though where appropriate, answers should be ex- act.

  1. Differentiate the function f (x) = e πe^2 −πeπ 2 e−π^2 +sin(π/8) with respect to^ x.
  2. What is the slope of the tangent line to f (x) = x^2 − 3 πx + 2 at x = 0?
  1. Which rule, (product, chain or quotient) is required to differentiate the function g(x) =

3 x^2 − 2 x + 1? Find its derivative.

  1. Which rule, (product, chain or quotient) is required to differentiate the function g(x) = 3ex^ sin(x)? Find its derivative.

Long Answer (20 points each) - show work and provide explana- tions, an answer without supporting work will not receive credit.

  1. A low flying jet aircraft covering a straight course is tracked by a radar station set 6 miles to one side of the flight path (see figure below). The radar can only measure the distance s from the station to the aircraft and the rate of change ds dt of the distance from the aircraft to the station. Use this information to determine the speed the aircraft (dx dt ) when s = 10 miles given that at this time ds dt = 800mph.
  1. Find the linear approximation to f (x) = xsin(x)^ at x = 1.