finals
Name: _____________________________ MAT 1022.E1 Final Exam Score: _________
Winter 2021
NOTE: Complete and return ONLY the answer sheet at the end of this exam.
I Matching
1. Optimization
a. [x^(n+1)]/(n+1) + C
2. Decreasing
b. F(x,y) = 4xy^3
3. Critical value
c. Relative highs or lows
4. Concave Up
d. C(x) + K
5. Concave Down
e. f ′ > 0
6. Inflection Point
f. Definite Integral Evaluation
7. Antiderivatives
g. f ( = 0 or Does Not Exist
8. Indefinite Integral for f(x)
h. e^x + C
9. Constant of Integration
i. Highs or Lows Overall
10. Definite Integral
j. ln x + C
11. Limits of Integration
k. f ″ < 0
12. Fundamental Theorem
l. F(x) if F((x) = f(x)
13. Stationary
m. The C in ( f(x)dx = F(x) + C
14. Local Extrema
n. #’s At Top and Bottom of Integral Sign
15. Global Extrema
o. f ( > 0
16. Integral of e^x
p. Family of Functions
17. Integral of dx/x
q. Both f ′ and f ″ Equal Zero
18. Integral of Marginal Cost
r. Not Changing
19. Increasing
s. Represents a Real Number
20.
Stationary inflection
t. f ′ < 0
21. Integral of x^n dx
u. Change in concavity
22. Function of two variables
v. Process of finding max & min
Note: There is an unwritten answer “e. None of these” for each problem in this section.
II. Multiple Choice
1. The critical value/s for y = x^3 – 3x^2 are:
a. 0 b. 2 c. 0,-2 d. 2,0
2. An inflection value for y = x^3 – 3x^2 is:
a. 1 b. -1 c. 0 d. 2
3. Over which interval is f(x) = x^3 – 12 x^2 + 36x + 1 decreasing?
a. (-(,2) b. (2,6) c. (6,() d.(-6,-2)
4. Use profit, P(x) = -0.01x^3 + 52.92x + 4500, to find the optimal value of x.
a. Infinite b. 1764 c. 42 d. 598176
5. For the function in problem #4 what is the optimal value of P?
a. ( b. 598176 c.1764 d. 42
6. Relative extrema for y = (x^2 + 5x + 3)/(x – 1) are located at:
a. (1,-2), (13,4) b. (4,1), (-2,13) c. (-2,1), (4,13) d. (1,4), (13,-2)
7. Find the absolute minimum for f(x) = x^4 – 4x^3 – 5.
a. –32 b. –180 c. 3 d. –21
8. Determine the indefinite integral: ( (4x^2 + 3x – 5) dx
a. 4x^3/3 + 3x^2/2 – 5 b. 8x + 3 c. 4x^3/3 + 3x^2/2 + C d. 4x^3/3 + 3x^2/2 –5x + C
9. What is C(x) if C’(x) = 3x^2 – 4x + 7 and fixed costs are $500?
a. 6x –4 b. x^3 – 2x^2 +7x + C c. x^3 – 2x^2 + 500 d. x^3 – 2x^2 + 7x + 500
10. Calculate the area below y = 4 – x^2 over the interval [0,2].
a. 8 b. 8/3 c. 5 d. 17/3
11. Give the indefinite integral for f(x)=e^x+x+1.
a. e^x+1
b. e^x+1+C
c. e^x+x^2/2+x
d. e^x+(1/2)x^2+x+C
12. Which is the indefinite integral of y=sqrtx
a. 1/2sqrtx+C
b. (2/3)x^(3/2)+C
c. x^(3/2)+C
d. sqrtx+C
13. The value of the definite integral for f(x)=x^3 from x=1 to x=2 is:
a.15
b. 5
c. 3.75
d.7
14. Choose the correct value for the definite integral of y=xe^(x^2) from x=0 to x=1.
a. e-1
b. e
c. e/2
d.(e-1)/2
III. True (T) / False (F)
1. The function, y = x^4 – 8x^3 + 18x^2 is concave downward on the interval (1,3).
2. Exact evaluation of (xe^(x^2) dx over the interval (0,1) gives (e-1)/2.
3. For ( (4/x) dx over the interval (1, 3) the value is 4.
4. Correct completion for the formula (e^x dx is e^x.
5. Indefinite integral and antiderivative are different functions.
6. If y’>0 and y”<0, then y will be concave downward and decreasing.
7. Absolute extrema will always be relative extrema, too.
8. Marginal revenue is the antiderivative of revenue.
9. Some extrema can be found by equating the derivative to zero.
10. An inflection point occurs when a second derivative equals zero.
11. Area under a curve, real number and definite integral are all synonymous.
12. In the formula ((1/x) dx the correct completion is ln x.
13. Completing the power rule for integrals (u^n du gives [u^(n+1)/(n+1)] + C.
14. Increasing and concave upward behavior by g(x) means g”(x)<0 and g’(x)>0.
Mat1022 Final Exam Winter 2021
Answer Sheet
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