Describe how the graph of y = x4 can be transformed to the graph of the given equation.
y = (x – 5)4 (5 points)
Use your calculator and a table of values to find the exact value of . (The limit as x approaches infinity) (5 points)
Use the graph below to evaluate :
Find the vertical asymptote(s) for the function . (5 points)
The end behavior of most closely matches which of the following? (5 points)
Which of the following functions is continuous at x = 2? (5 points)
Evaluate . (5 points)
Find f ‘(x) for f(x) = 8x3 + 2x2 – 8x + 10. (5 points)
Find g ‘(x) for g(x) = sin(6x). (5 points)
Where is the second derivative of y = 3xe-x equal to 0? (5 points)
If f(x) = arcsin(2x), then f ‘(x) = ? (5 points)
The graph of the derivative, f ‘(x) is shown below. On what interval is the graph of f (x) increasing?
A particle moves along the x-axis with position function s(t) = esin(x). How many times in the interval [0, 2π] is the velocity equal to 0? (5 points)
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)
Use the graph of f(x) = |x(x2 – 1)| to find how many numbers in the interval [0.5, 0.75] satisfy the conclusion of the Mean Value Theorem. (5 points)