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6 Questions Exam 1 - Calculus I | MATH 170, Exams of Calculus

Boise State University (BSU)Calculus
Prof. Richard Ketchersid

Material Type: Exam; Professor: Ketchersid; Class: Calculus I; Subject: Mathematics; University: Boise State University; Term: Fall 2008;

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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Name:
Exam 1 - Math 170
Oct 1, 2008
R. Ketchersid
Instructions. Show all work for any partial credit. Where appropriate indicate your final answer
by putting a box around the answer. Do not leave two answers and expect me to pick the correct
one for you. Feel free to use your calculator to check answers, but I want exact solutions to all
problems. If anything is unclear ask me about it.
1. [10pts] Compute f0(x) for f(x) = 3x2+ 1 using one of the two limit definitions of derivative
given in class.
2. [5pts] If you zoom in at (1,4) on the graph of y= 3x2+ 1, then the graph looks like a straight
line. What is the equation of this line?
3. [5pts] What does it mean to say “f(x) is continuous at x=a”?
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Download 6 Questions Exam 1 - Calculus I | MATH 170 and more Exams Calculus in PDF only on Docsity!

Name:

Exam 1 - Math 170

Oct 1, 2008 R. Ketchersid

Instructions. Show all work for any partial credit. Where appropriate indicate your final answer by putting a box around the answer. Do not leave two answers and expect me to pick the correct one for you. Feel free to use your calculator to check answers, but I want exact solutions to all problems. If anything is unclear ask me about it.

  1. [10pts] Compute f ′(x) for f (x) = 3x^2 + 1 using one of the two limit definitions of derivative given in class.
  2. [5pts] If you zoom in at (1, 4) on the graph of y = 3x^2 + 1, then the graph looks like a straight line. What is the equation of this line?
  3. [5pts] What does it mean to say “f (x) is continuous at x = a”?
  1. [10pts] Consider the function

f (x) = x^2 − 9 x^2 + x − 6

You don’t need to show work on each part, you will either get it correct or not.

a) [2pts] Where is f (x) continuous? (Use interval notation.)

b) [2pts] Where is f (x) > 0? Use a sign diagram for f (x).

c) [2pts] Are there any vertical asymptotes? If so what are they?

d) [2pts] Are there any horizontal asymptotes? If so what are they?

e) [2pts] Sketch the vertical and horizontal asymptotes and roots of f (x). Using this information and your sign diagram sketch a rough guess at what the function looks like.