Calc Multiple Choice

Calc Multiple Choice

1.  Describe how the graph of y = x4 can be transformed to the graph of the given equation.

y = (x – 2)4 + 9 (5 points)

 
Shift the graph of y = x4 right 2 units and up 9 units.
Shift the graph of y = x4 left 2 units and down 9 units.
Shift the graph of y = x4 right 2 units and down 9 units.
Shift the graph of y = x4 left 2 units and up 9 units.

2.  Use your calculator and a table of values to find the exact value of limit as x goes to 0 of the quotient of sine of x squared and x . (The limit as x approaches zero) (5 points)
 

3.  Use the graph below to evaluate the limit as x approaches 2 of f of x :

Graph of a function that increases for x greater than or equal to 0 and less than 2 and decreases for x greater than 2 and less than or equal to 4. The point (2, 3) is marked on the graph (5 points)

 
0
4
3
2

4.  Find the vertical asymptote(s) for the function the quotient of the quantity x plus 5 and the quantity x squared plus 25 . (5 points)
 
x = -5, 5
y = 0
x = -1
x = 5

5.  The end behavior of f of x equals the quotient of the quantity 5 plus 2 times x squared and the quantity x squared minus 25 most closely matches which of the following? (5 points)
 
y = 0
y = 1
y = 2
y = -18

6.  Which of the following functions is continuous at x = 2? (5 points)
 
f of x equals the quotient of the quantity x squared minus 4 and the quantity x minus 2 for x not equal to 2 and equals 4 for x equals 2
f of x equals the quotient of the quantity x squared minus 4 and the quantity x minus 2 for x not equal to 2 and equals 3 for x equals 2
f of x equals the quotient of the quantity x squared minus 4 and the quantity x minus 2
All are continuous at x = 2

7.  Evaluate the limit as h goes to 0 of the quotient of the quantity the 5th power of 3 plus h minus 81 and h . (5 points)
 
108
3
81
Does not exist

8.  Find f ‘(x) for f(x) = 8×3 + 2×2 – 8x + 10. (5 points)
 
None of these
f ‘(x) = 24×2 + 4x – 8
f ‘(x) = 24×2 + 4x – 8 + 10
f ‘(x) = 24x + 4x – 10

9.  Find g ‘(x) for g(x) = sec(2x). (5 points)
 
g ‘(x) = 2tan2(2x)
g ‘(x) = 2sec(2x)tan(2x)
g ‘(x) = 2sec(2x)
g ‘(x) = 2sec2(2x)

10.  Where is the second derivative of y = 2xe-x equal to 0? (5 points)
 
2
4
1
0

11.  If f(x) = arctan(2x), then f ‘(x) = ? (5 points)
 
the quotient of 2 and the quantity 1 plus 4 times x squared
the quotient of 1 and the quantity 1 plus 4 times x squared
the quotient of 1 and the quantity 1 plus 4 times x squared
the quotient of 2 and the quantity 1 plus 2 times x squared

12.  The graph of the derivative, f ‘(x) is shown below. On what interval is the graph of f (x) concave up?

graph is a parabola with x intercepts at x equals negative 4 and 2 and y intercept at y equals negative 2 (5 points)

 
Concave up on (-∞, -1)
Concave up on (-6, -2)
Concave up on (-∞, -∞)
Concave up on (-1, ∞)

13.  A particle moves along the x-axis with position function s(t) = ecos(x). How many times in the interval [0, 2π] is the velocity equal to 0? (5 points)
 
More than 3
2
3
1

14.  An ice block is melting so that the length of each side is changing at the rate of 1.5 inches per hour. How fast is the surface area of the ice cube changing at the instant the ice block has a side length of 2 inches? (5 points)
 
-18 in2/hour
-36 in2/hour
-12 in2/hour
-24 in2/hour

15.  If f(x) = |(x2 – 4)(x2 + 2)|, how many numbers in the interval [0, 1] satisfy the conclusion of the Mean Value Theorem? (5 points)
 
3
None
2
1


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