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MAT 211 Calculus Final Exam Solutions - Fall 2003, Exams of Mathematics

The solutions to the calculus final exam for the mat 211 course taught by professor jones in fall 2003. It includes answers to 25 calculus problems covering topics such as exponential functions, logarithms, derivatives, and critical points.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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MAT 211 Jones - Fall 2003
Calculus
Final Exam
Choose the best answer - record your answer on the answer sheet.
1. Assume the graph of the exponential function passes through the points
and . Find the values of k and a.
(a)
2. Express in terms of the natural logarithm and find the domain and range of
.
(b)
3. Evaluate, if possible: .
(a)
4. Evaluate, if possible: .
(c)
5. Evaluate, if possible: .
(c)
6. Find the intervals on which is continuous.
(d)
7. Find the equation for the tangent line to the curve at the point
.
(a)
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MAT 211 Jones - Fall 2003 Calculus Final Exam

Choose the best answer - record your answer on the answer sheet.

  1. Assume the graph of the exponential function passes through the points and. Find the values of k and a. (a)
  2. Express in terms of the natural logarithm and find the domain and range of . (b)
  3. Evaluate, if possible:.

(a)

  1. Evaluate, if possible:.

(c)

  1. Evaluate, if possible:.

(c)

  1. Find the intervals on which is continuous.

(d)

  1. Find the equation for the tangent line to the curve at the point . (a)
  1. Find equations of all tangents to the curve that have slope.

(c)

  1. Find the derivative of.

(b)

  1. Find the derivative of.

(a)

  1. Find the derivative of.

(b)

  1. Find the derivative of.

(b)

  1. Find the second derivative of. (b)
  2. Assume that y is a function of x. Find if.

(b)

  1. Determine the interval(s) on which is decreasing if. (c)
  1. Which of the following must be true so that the function has a

local maximum value at the stationary point? (Hint: )

(d)

  1. Let be a polynomial function such that. The point (2,5) is a ____________________ of the graph of. (b) relative minimum