Repeat Problem 79 if the balloon is 1,024 feet above the ground when the ball is dropped. Data from Problem 79: A ball dropped from a balloon falls y = 16x2 feet in x seconds. If the balloon is 576 feet above the ground when the ball is dropped, when does the ball hit the ground? What is the velocity of the ball at the instant it hits the ground?
> Compute the probability of event E if the odds in favor of E are. Answer:
> Can a cubic polynomial function have more than two horizontal tangents? Explain.
> Now that you know how to find derivatives, explain why it is no longer necessary for you to memorize the formula for the x coordinate of the vertex of a parabola.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> Require the use of a graphing calculator. For each problem, find ’(x) and approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line.
> If an object moves along the y axis (marked in feet) so that its position at time x (in seconds) is given by the indicated functions. Find (A) The instantaneous velocity function v = ’(x) (B) The velocity when x = 0
> If an object moves along the y axis (marked in feet) so that its position at time x (in seconds) is given by the indicated functions. Find (A) The instantaneous velocity function v = ’(x) (B) The velocity when x = 0
> Find (A) ï‚¦ï€ (x) (B) The slope of the graph of  at x = 2 and x = 4 (C) The equations of the tangent lines at x = 2 and x = 4 (D) The value(s) of x where the tangent line is horizontal
> Find (A) ï‚¦ï€ (x) (B) The slope of the graph of  at x = 2 and x = 4 (C) The equations of the tangent lines at x = 2 and x = 4 (D) The value(s) of x where the tangent line is horizontal
> Suppose that 6 people check their coats in a checkroom. If all claim checks are lost and the 6 coats are randomly returned, what is the probability that all the people will get their own coats back?
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Given the following probabilities for an event E, find the odds for and against E:
> Write the expression as a quotient of integers, reduced to lowest terms.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Refer to functions f and g that satisfy ’ (2) = 3 and g’ (2) = -1. In each problem, find h’ (2) for the indicated function h.
> Refer to functions f and g that satisfy ’ (2) = 3 and g’ (2) = -1. In each problem, find h’ (2) for the indicated function h.
> Refer to functions f and g that satisfy ’ (2) = 3 and g’ (2) = -1. In each problem, find h’ (2) for the indicated function h.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> Find the indicated derivatives.
> In a three-way race for the U.S. Senate, polls indicate that the two leading candidates are running neck-and-neck, while the third candidate is receiving half the support of either of the others. Registered voters are chosen at random and asked which of
> Find the indicated derivatives.
> Find the indicated derivatives. g′(x) for g(x) = x9
> Find the indicated derivatives. y′ for y = x8
> Find the indicated derivatives.
> Write the expression in the form a + b1n where a and b are reduced fractions and n is an integer
> Write the expression in the form a + b1n where a and b are reduced fractions and n is an integer
> Find the slope of the line through the given points. Write the slope as a reduced fraction, and also give its decimal form. Answer:
> Find the slope of the line through the given points. Write the slope as a reduced fraction, and also give its decimal form.
> The body temperature (in degrees Fahrenheit) of a patient t hours after taking a fever-reducing drug is given by (A) Use the four-step process to find F= (t). (B) Find F(3) and F= (3). Write a brief verbal interpretation of these results.
> Refer to the data in Table 1. (A) Let x represent time (in years) with x = 0 corresponding to 2000, and let y represent the corresponding commercial sales. Enter the appropriate data set in a graphing calculator and find a quadratic regression equation
> Use the equally likely sample space in Example 2 to compute the probability of the following events: The number on the first die is even or the number on the second die is even.
> The U.S. consumption of refined copper (in thousands of metric tons) is given approximately by P(t) = 48t2 - 37t + 1,698 where t is time in years and t = 0 corresponds to 2010. (A) Use the four-step process to find p′(t). (B) Find the annual consumptio
> A company’s total sales (in millions of dollars) t months from now are given by S(t) = √t + 8 (A) Use the four-step process to find S′1t2. (B) Find S(9) and S′(9). Write a brief verbal interpretation of these results. (C) Use the results in part (B)
> The profit (in dollars) from the sale of x infant car seats is given by P(x) = 45x - 0.025x2 - 5,000 0 ≤ x ≤ 2,400 (A) Find the average change in profit if production is changed from 800 car seats to 850 car seats. (B) Use the four-step process to fin
> Determine whether  is differentiable at x = 0 by considering
> Determine whether  is differentiable at x = 0 by considering (x) = x2/3
> Determine whether  is differentiable at x = 0 by considering (x) = 1 - | x |
> sketch the graph of  and determine where  is nondifferentiable.
> sketch the graph of  and determine where  is nondifferentiable.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the graph of f has a sharp corner at x = a, then f is not continuous at x = a
> Refer to the description of a standard deck of 52 cards and Figure 4 on page 384. An experiment consists of dealing 5 cards from a standard 52-card deck. In Problems what is the probability of being dealt. Figure 4: 5 nonface cards.
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. if a function f is differentiable on the interval (a, b), then f is continuous on (a, b)
> Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If (x) = mx + b is a linear function, then ’(x) = m.
> Let (x) = -x2 , g(x) = -x2 - 1, and h(x) = -x2 + 2. (A) How are the graphs of these functions related? How would you expect the derivatives of these functions to be related? (B) Use the four-step process to find the derivative of m(x) = -x2 + C, whe
> Repeat Problem 59 with (x) = 8x2 - 4x. Data from Problem 59: If an object moves along a line so that it is at y = (x) = 4x2 - 2x at time x (in seconds), find the instantaneous velocity function v = (x) and find the velocity at times x = 1, 3, and 5
> (A) Find = (x). (B) Find the slopes of the lines tangent to the graph of at x = 0, 2, and 4. (C) Graph and sketch in the tangent lines at x = 0, 2, and 4. (x) = 4x - x2 + 1
> Refer to the function F in the graph shown. Use the graph to determine whether F’(x) exists at each indicated value of x x = h
> Refer to the function F in the graph shown. Use the graph to determine whether F’(x) exists at each indicated value of x x = .
> Refer to the function F in the graph shown. Use the graph to determine whether F’(x) exists at each indicated value of x x = d
> Refer to the function F in the graph shown. Use the graph to determine whether F’(x) exists at each indicated value of x x = b
> suppose an object moves along the y axis so that its location is y = (x) = x2 + x at time x (y is in meters and x is in seconds). Find (A) The average velocity (the average rate of change of y with respect to x) for x changing from 2 to 4 seconds (B) T
> Use the equally likely sample space in Example 2 to compute the probability of the following events: A sum that is greater than 9.
> Refer to the graph of y = ( (x) = x2 + x shown. (A) Find the slope of the secant line joining (2, (2)) and (4, (4)). (B) Find the slope of the secant line joining (2, (2)) and (2 + h, ï&#
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Refer to the description of a standard deck of 52 cards and Figure 4 on page 384. An experiment consists of dealing 5 cards from a standard 52-card deck. what is the probability of being dealt. Figure 4: 5 Hearts?/
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> Use the four-step process to find ( = (x) and then find ( = (1) , ( = (2), and ( = (3).
> For ((x) = x4 , the instantaneous rate of change is known to be -4 at x = -1. Find the equation of the tangent line to the graph of y = ((x) at the point with x coordinate -1.
> For( (x) = 1 / + x2, the slope of the graph of y = ( (x) is known to be -0.16 at the point with x coordinate 2. Find the equation of the tangent line at that point.
> Four hours after the start of a 600-mile auto race, a driver’s velocity is 150 miles per hour as she completes the 352nd lap on a 1.5-mile track.
> Find the indicated quantities for f(x) = 3x2 .
>
> Use interval notation to specify the given interval.
> If the probability is .03 that an automobile tire fails in less than 50,000 miles, what is the probability that the tire does not fail in 50,000 miles?
> Use interval notation to specify the given interval.
> Use interval notation to specify the given interval.
> Use interval notation to specify the given interval. The set of all real numbers from -8 to -4, excluding -8 but including -4
> The graph shown represents the history of a person learning the material on limits and continuity in this book. At time t2, the student’s mind goes blank during a quiz. At time t4, the instructor explains a concept particularly well, th
> An office equipment rental and leasing company rents copiers for $10 per day (and any fraction thereof) or for $50 per 7-day week. Let C1x2 be the cost of renting a copier for x days.
> Table 2 shows the rates for natural gas charged by the Middle Tennessee Natural Gas Utility District during winter months. The base charge is a fixed monthly charge, independent of the amount of gas used per month. (A) Write a piecewise definition of t
> Discuss the differences between the function S(x) = 15 + 10 [x] and R(x) defined in Problem 90. (The symbol [x] is defined in problems 75 and 76.)
> A bike rental service charges $15 for the first hour (or any fraction thereof) and $10 for each additional hour (or fraction thereof) up to a maximum of 8 hours. (A) Write a piecewise definition of the charge R(x) for a rental lasting x hours. (B) Grap
> The function ((x) = 6 / (x – 4) satisfies ((2) = -3 and ((7) = 2. Is ( equal to 0 anywhere on the interval (0, 9)? Does this contradict Theorem 2? Explain.
> Sketch a possible graph of a function ( that is continuous for all real numbers and satisfies the given conditions. Find the x intercepts of (. ((x) > 0 on (1 - ∞, -3) and (2, 7); ( (x) < 0 on (-3, 2) and ( 7 , ∞)
> A keypad at the entrance of a building has 10 buttons labeled 0 through 9. What is the probability of a person correctly guessing a 4-digit entry code if they know that no digits repeat
