Absolute value inequalities are often used to represent measurement error. For example, suppose that a machine is calibrated to dispense 8 fl oz of orange juice with a measurement error of on more than 0.05 fl oz. If x represents the actual amount of orange juice poured into the bottle, then x is a solution to the inequality x − 8 ≤ 0.05. For Exercises 79-82. a. Write an absolute value inequality to represent each statement. b. Solve the inequality. Write the solution set in interval notation. The variation between the measured value t and 60 min is less than 0.2 min.
Absolute value inequalities are often used to represent measurement error. For example, suppose that a machine is calibrated to dispense 8 fl oz of orange juice with a measurement error of on more than 0.05 fl oz. If x represents the actual amount of orange juice poured into the bottle, then x is a solution to the inequality x − 8 ≤ 0.05. For Exercises 79-82. a. Write an absolute value inequality to represent each statement. b. Solve the inequality. Write the solution set in interval notation. The variation between the measured value t and 60 min is less than 0.2 min.
Absolute value inequalities are often used to represent measurement error. For example, suppose that a machine is calibrated to dispense 8 fl oz of orange juice with a measurement error of on more than 0.05 fl oz. If
x
represents the actual amount of orange juice poured into the bottle, then
x
is a solution to the inequality
x
−
8
≤
0.05.
For Exercises 79-82.
a. Write an absolute value inequality to represent each statement.
b. Solve the inequality. Write the solution set in interval notation.
The variation between the measured value
t
and
60
min is less than 0.2 min.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Elementary Statistics: Picturing the World (7th Edition)
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