Math 220–Test 1
University of Illinois, September 19, 2008
NAME:
SECTION:
No calculators, notes, text or phones during the exam.
1. (10)
2. (8)
3. (10)
4. (10)
5. (8)
6. (8)
7. (6)
8. (10)
Total. (70)
1
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8 Questions on Basic Calculus - Examination 1 | MATH 220, Exams of Calculus
Material Type: Exam; Class: Calculus; Subject: Mathematics; University: University of Illinois - Urbana-Champaign; Term: Fall 2008;
Typology: Exams
Pre 2010
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Math 220–Test 1
University of Illinois, September 19, 2008
NAME:
SECTION:
No calculators, notes, text or phones during the exam.
Total. (70)
- Short answer. 10 points, 2/2/
1a. Compute cos(sin−^1 ( 15 )).
1.b Compute log 2 8.
1c. Consider the following diagram in the Cartesian plane:
Why is this the graph of a function?
What is the domain of this function?
What is the range of this function?
Is this function invertible? Why or why not?
- Derivatives. 10 points, 4/4/
4a. What is the definition of the derivative of a function f (x) at a?
4b. Use the definition of the derivative to show the derivative of f (x) = x^2 + 2x + 1 is 2 x + 2.
4c. Compute the derivative of f (x) = 2 x
(^2) +2x+ x by any means we’ve covered in class.
- Tangent lines. 8 points, 2/
5a. List the points A, B, C and D in order of increasing slope of the tangent line.
5b. (HW) Give the equation of the tangent line to f (x) = 4
x − 2 x at the point (4, 0).
- 8 points (HW)
Suppose a state’s income tax code states the tax liability on x dollars of taxable income is given by
T (x) =
- 14 x if 0 ≤ x < 10 , 000 1500 + 0. 21 x if 10, 000 ≤ x
Compute limx→ 0 + T (x) and limx→ 10 , 000 T (x) (be sure to explain your result). Why is this bad?
- 10 points (HW)
A metal washer of (outer) radius r inches weighs 2r^3 ounces. A company manufactures 2-inch washers for different customers who have different error tolerances. If the customer demands a washer of weight 8 ± ǫ ounces, what is the error tolerance for the radius? That is, how close does the radius need to be to 2 inches to guarantee a weight within 8 ± ǫ ounces?