MAT1308 A INTRODUCTION TO CALCULUS Homework 1
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MAT1308 A INTRODUCTION TO CALCULUS
Homework 1 due Friday, September 22, 2023 before 11:30 PM
QUESTIONS
1. [2pts]Find the domain of the following function : 
2. School Construction Costs: The cost, in millions of dollars, of building a two -story high school in Ontario was estimated to be
C(x) = 1.7 + 0.12x − 0.0001x2 (20 ≤ x ≤ 400),
where x is the number of thousands of square feet. Suppose that you are contemplating
building a for-profit two story highschool and estimate that your total revenue will be $ 0.1 million per thousand square feet.
(a) [1pt] What is the profit function.
(b) [2pts] What size school should you build to break even?
(c) [2pts] What size school should you build to minimize your profit?
(d) [1pt] What is the minimum profit?
3. Evaluate the following limits if they exist.
(a) [2pts] 
(b) [2pts] 
4. Consider the following rational function: 
(a) [2pts] What is the domain of f ?
(b) [1pt] Does the graph off have any holes? If so, what are their coordinates?
(c) [2pts] Does the graph off have any vertical asymptotes? If so, what are they?
(d) [1pt] Does the graph off have any horizontal asymptotes? If so, what are they?
5. [2pts] Consider the following function:
Find the value of c for which this function is continuous everywhere on (−∞ , +∞ ).
2023-09-22