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Math 105 Exam 1 - October 5, 2007: Solutions for Selected Problems, Exams of Calculus

Birla Institute of Technology and ScienceCalculus

Solutions for selected problems from the math 105 exam 1 held on october 5, 2007. The problems involve finding the domain of a function, determining if a number is in the range, finding position functions, identifying local maximum points and inflection points, ordering function values, and determining if a function is even or odd. Students can use this document as a reference for understanding the solutions to these problems.

Typology: Exams

2012/2013

Uploaded on 03/06/2013

ekan
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NAME:
Math 105 - Exam 1 - October 5, 2007
Instructions: Show all of your work and circle your final answers. Calculators are allowed, but notes and
books are not.
1. (10 points) Suppose f(x) = 2x−3
x2
−2x.
(a) What is the domain of f(x)? (Write your answer in interval notation.)
(b) Is 1 in the range of f(x)? Explain.
2. (6 points) Suppose that the velocity of an object at time tis given by the function v(t) = 3
√t+ 4. Find
all possible corresponding position functions p(t).
pf3
pf4
pf5

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Download Math 105 Exam 1 - October 5, 2007: Solutions for Selected Problems and more Exams Calculus in PDF only on Docsity!

NAME:

Math 105 - Exam 1 - October 5, 2007

Instructions: Show all of your work and circle your final answers. Calculators are allowed, but notes and books are not.

  1. (10 points) Suppose f (x) =

2 x − 3 x^2 − 2 x

(a) What is the domain of f (x)? (Write your answer in interval notation.)

(b) Is 1 in the range of f (x)? Explain.

  1. (6 points) Suppose that the velocity of an object at time t is given by the function v(t) = 3

t + 4. Find all possible corresponding position functions p(t).

  1. (14 points) Let f (x) = 1 − 2 x^2.

(a) Find the average rate of change of f from x = 0 to x = 2.

(b) What does your answer to (a) represent graphically?

(c) Using the limit definition of the derivative, find f ′(3).