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Chapter

Section

Problem 2E:

If f(x)=x2xx1andg(x)=x is it true that f = g?

Problem 3E:

The graph of a function f is given. (a) State the value of f(1). (b) Estimate the value of f(1). (c)...

Problem 4E:

The graphs of f and g are given. (a) State the values of f(4) and g(3). (b) For what values of x is...

Problem 5E:

Figure 1 was recorded by an instrument operated by the California Department of Mines and Geology at...

Problem 7E:

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...

Problem 8E:

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...

Problem 9E:

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of...

Problem 10E:

Problem 11E:

Shown is a graph of the global average temperature T during the 20th century. Estimate the...

Problem 12E:

Trees grow faster and form wider rings in warm years and grow more slowly and form narrower rings in...

Problem 13E:

You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a...

Problem 14E:

Three runners compete in a 100-meter race. The graph depicts the distance run as a function of time...

Problem 15E:

The graph shows the power consumption for a day in September in San Francisco. (P is measured in...

Problem 16E:

Sketch a rough graph of the number of hours of daylight as a function of the time of year.

Problem 17E:

Sketch a rough graph of the outdoor temperature as a function of time during a typical spring day.

Problem 18E:

Sketch a rough graph of the market value of a new car as a function of time for a period of 20...

Problem 19E:

Sketch the graph of the amount of a particular brand of coffee sold by a store as a function of the...

Problem 20E:

You place a frozen pie in an oven and bake it for an hour. Then you take it out and let it cool...

Problem 21E:

A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass...

Problem 22E:

An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If...

Problem 23E:

Temperature readings T (in F) were recorded every two hours from midnight to 2:00 PM in Atlanta on...

Problem 24E:

Researchers measured the blood alcohol concentration (BAC) of eight adult male subjects after rapid...

Problem 25E:

If f(x) = 3x2 x + 2, find f(2), f(2), f(a), f(a), f(a + 1), 2f(a), f(2a), f(a2), [f(a)]2, and f(a +...

Problem 26E:

A spherical balloon with radius r inches has volume V(r)=43r3. Find a function that represents the...

Problem 29E:

Evaluate the difference quotient for the given function. Simplify your answer. 29. f(x)=1x,...

Problem 30E:

Evaluate the difference quotient for the given function. Simplify your answer. 30. f(x)=x+3x+1,...

Problem 31E:

Find the domain of the function. 31. f(x)=x+4x29

Problem 32E:

Find the domain of the function. 32. f(x)=2x35x2+x6

Problem 33E:

Find the domain of the function. 33. f(t)=2t13

Problem 34E:

Find the domain of the function. 34. g(t)=3t2+t

Problem 35E:

Find the domain of the function. 35. h(x)=1x25x4

Problem 36E:

Find the domain of the function. 36. f(u)=u+11+1u+1

Problem 37E:

Find the domain of the function. 37. F(p)=2p

Problem 41E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 42E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 43E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 44E:

Evaluate f(3), f(0), and f(2) for the piecewise defined function. Then sketch the graph of the...

Problem 45E:

Sketch the graph of the function. 45. f(x) = x + |x|

Problem 46E:

Sketch the graph of the function. 46. f(x) = |x + 2|

Problem 47E:

Sketch the graph of the function. 47. g(t) = |1 3t|

Problem 50E:

Sketch the graph of the function. 50. g(x) = ||x| 1|

Problem 51E:

Find an expression for the function whose graph is the given curve. 51. The line segment joining the...

Problem 52E:

Find an expression for the function whose graph is the given curve. 52. The line segment joining the...

Problem 53E:

Find an expression for the function whose graph is the given curve. 53. The bottom half of the...

Problem 54E:

Find an expression for the function whose graph is the given curve. 54. The top half of the circle...

Problem 57E:

Find a formula for the described function and state its domain. 57. A rectangle has perimeter 20 m....

Problem 58E:

Find a formula for the described function and state its domain. 58. A rectangle has area 16 m2....

Problem 59E:

Find a formula for the described function and state its domain. 59. Express the area of an...

Problem 60E:

Find a formula for the described function and state its domain. 60. A closed rectangular box with...

Problem 61E:

Find a formula for the described function and state its domain. 61. An open rectangular box with...

Problem 62E:

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the...

Problem 63E:

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12...

Problem 64E:

A cell phone plan has a basic charge of 35 a month. The plan includes 400 free minutes and charges...

Problem 65E:

In a certain state the maximum speed permitted on freeways is 65 mi/h and the minimum speed is 40...

Problem 66E:

An electricity company charges its customers a base rate of 10 a month, plus 6 cents per...

Problem 67E:

In a certain country, income tax is assessed as follows. There is no tax on income up to10,000. Any...

Problem 68E:

The functions in Example 10 and Exercise 67 are called step function because their graphs look like...

Problem 69E:

Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your...

Problem 70E:

Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your...

Problem 71E:

(a) If the point (5, 3) is on the graph of an even function, what other point must also be on the...

Problem 72E:

A function f has domain [5, 5] and a portion of its graph is shown. (a) Complete the graph of f if...

Problem 73E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 74E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 75E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 76E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 77E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

Problem 78E:

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check...

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(a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...Explain what each of the following means and illustrate with sketch. (a) limxaf(x)=L (b)...State each differentiation rule both in symbols and in words. (a) The Power Rule (b) The Constant...Explain the difference between an absolute maximum and a local maximum. Illustrate with a sketch.(a) Write an expression for a Riemann sum of a function f. Explain the meaning of the notation that...(a) Draw two typical curves y = f(x) and y = g(x), where f(x) g(x) for a x b. Show how to...Stale the rule for integration by parts. In practice, how do you use it?(a) How is the length of a curve defined? (b) Write an expression for the length of a smooth curve...(a) What is a differential equation? (b) What is the order of a differential equation? (c) What is...

(a) What is a parametric curve? (b) How do you sketch a parametric curve?(a) What is a convergent sequence? (b) What is a convergent series? (c) What does limnan= 3 mean?...What is the difference between a vector and a scalar?What is a vector function? How do you find its derivative and its integral?(a) What is a function of two variables? (b) Describe three methods for visualizing a function of...Suppose f is a continuous function defined on a rectangle R = [a, b] [c, d]. (a) Write an...What is a vector field? Give three examples that have physical meaning.(a) Write the general form of a second-order homogeneous linear differential equation with constant...

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