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1. The table shown gives some evidence that which mathematical statement is true?
x 7 7.9 7.9999 8.001 8.1 9
f(x) −6 −6.2 −6.297 −6.303 −6.37 −7
2. Which of these is a tangent line to y = −x2 at x = 4?
A. y = −8x + 16
B. y = −16x + 72
C. y = −8x + 80
D. y = −16x + 80
3. If exists, is ƒ therefore continuous at x = a?
A. No
B.
C. If ƒ(a) also exists, yes
D. Yes
4. Where is y = lnx discontinuous?
A. Only where it's undefined, which is for all x < 0
B. Nowhere. It's a smooth curve on its entire domain.
C. Only at zero
D. Only where it's undefined, which is for all
5.
A. 30x
B. 30x2
C. 30
D. 10x2
6. Compute .
A. 4
B. 6
C. Doesn't exist
D. 1/9
7. Compute .
A. 4
B. 9
C. 6
D. 1/9
8. What is the slope of the tangent line to
A. 1/6
B. −1/9
C. −1/3
D. 1
9. Compute .
A. Doesn't exist
B. 0
C. 1
D. 1/2
10. Estimate from the graph below.
A. 2.5
B. 2
C. 4.3
D. 2.8
11. At which points is the function shown in the graph discontinuous?
A. 1,3
B. Nowhere
C. 3.5
D. −3,−1,1,3
12. Compute .
A. 0.1
B. 0.11
C. Doesn't exist
D. 0.01
13. Let . Is there a value of a that would make ƒ(x) continuous everywhere?
A. Yes, a = e.
B. Yes, a = 1.
C. No
D. Yes, a = 0.
14. Find the average velocity from time t = 0 to t = 1 of a car whose position p(t) along a horizontal track is given by the equation p(t) = 4 − (t − 2)2.
A. 3
B. 2
C. 4
D. 1
15. Consider the figure shown. What is the value of ?
A. 0
B. 4
C. Doesn't exist
D. 3
16. Compute .
A. Doesn't exist
B. 2
C. 21/2
D. 0
17. Compute .
A. Doesn't exist
B. 3
C. −1
D. 6
18. Where is discontinuous?
19.
A. 3x
B. 13
C. x
D. 3
20. The area of a square with side length x is x2. What is the instantaneous rate of change in area if x is 5 and increasing?
A. 10
B. 25
C. 20
D. 5
