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7 Problems on Exam 3 for Calculus and Analytic Geometry I | MAT 250, Exams of Analytical Geometry and Calculus

Murray State UniversityAnalytical Geometry and Calculus

Material Type: Exam; Class: Calculus and Analytical Geometry I; Subject: MAT Mathematics; University: Murray State University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 08/17/2009

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koofers-user-zfn-1 🇺🇸

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Spring ’05/MAT 250/Exam 3 Name: Show all your work.
1. (6pts) The graph of the function fis given.
a) State where fhas an absolute minimum and maximum value, and what the value is.
b) State where fhas a local minimum and maximum value, and what the value is.
1-1-3 3
1
-2
2
3
-2
2. (9pts) Use L’Hospital’s rule to find the limits:
a) lim
x→0
1−cos x
x2=
b) lim
x→0(1 −2x)1
x=
pf3
pf4

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Download 7 Problems on Exam 3 for Calculus and Analytic Geometry I | MAT 250 and more Exams Analytical Geometry and Calculus in PDF only on Docsity!

Spring ’05/MAT 250/Exam 3 Name: Show all your work.

  1. (6pts) The graph of the function f is given. a) State where f has an absolute minimum and maximum value, and what the value is. b) State where f has a local minimum and maximum value, and what the value is.

-3 -1 1 3

1

-

2

3

-

  1. (9pts) Use L’Hospital’s rule to find the limits:

a) lim x→ 0

1 − cos x x^2

b) lim x→ 0 (1 − 2 x)

1 x (^) =

  1. (10pts) Let f (x) = ln(x^2 + 4). a) Find the intervals of increase/decrease and where f has a local maximum and minimum. b) Find the intervals where f is concave up or down. c) Use your calculator and the results of a) and b) to accurately sketch the graph of f.
  2. (5pts) Suppose that for a continuous and differentiable function f we have − 2 ≤ f ′(x) ≤ 3 for all x in [1, 4] and f (1) = 7. Use the Mean Value Theorem to show that 1 ≤ f (1) ≤ 16.
  1. (7pts) Use the graph of f to sketch the graphs of f ′^ and f ′′.

a b c

Bonus. (5pts) Use Rolle’s theorem to show that the equation 2x + cos x = 0 has at most one solution.