Calculus: Concepts and Applications 2nd Edition solutions

Calculus: Concepts and Applications 2
Bungee Problem: Lee Per attaches himself to a strong bungee cord and jumps off a bridge. At time t = 3 s, the cord first becomes taut. From that time on, Lees distance, d, in feet, from the river below the bridge is given by the equation d = 90 80 sin [1.2 (t 3)] a. How far is Lee from the water wh

Calculus: Concepts and Applications 2
Pizza Delivery Problem: Ida Livermore starts off on her route. She records her trucks speed, v(t), in mi/h, at various times, t, in seconds, since she started. a. Show Ida that these data fit the equation v(t) = 5t1/2. t (s) v (t) (mi/h) 0 0 1 5 4 10 9 15 16 20 b. The trucks acceleration, a(t), is th

Calculus: Concepts and Applications 2
Rectangle Problem: A rectangle of length L and width W has a constant area of 1200 in.2. The length changes at a rate of dL/dt inches per minute. a. Find dW/dt in terms of W and dL/dt. b. At a particular instant, the length is increasing at 6 in./min and the width is decreasing at 2 in./min. Find the

Calculus: Concepts and Applications 2
For Problems 330, find the indicated limit. Use lHospitals rule if necessary.

Calculus: Concepts and Applications 2
Quartic Parabola Tank Problem: A water storage tank has the shape of the surface formed by rotating about the y-axis the graph of y = x4 + 5, where x and y are in meters (Figure 10-5a). At what rate is the depth of the water changing when the water is 3 m deep in the tank and draining at 0.7 m3/min?

Calculus: Concepts and Applications 2
Tin Can Problem: A popular size of tin can with normal proportions has diameter 7.3 cm and height 10.6 cm (Figure 8-3r). Figure 8-3r a. What is its volume? b. The volume is to be kept the same, but the proportions are to be changed. Write an equation expressing total surface of the can (lateral surfa

Calculus: Concepts and Applications 2
Conical Water Tank Problem: The water tank shown in Figure 4-9i has diameter 6 m and depth 5 m . Figure 4-9i a. If the water is 3 m deep, and is rising at 5 m/h, at what rate is the volume changing? b. If the water is pumped out at 2 m3/h, at what rate is the depth changing i. When the water is 4 m d

Calculus: Concepts and Applications 2
For Problems 116, evaluate the integral.

Calculus: Concepts and Applications 2
Fox Population Problem: The population of foxes in a particular region varies periodically due to fluctuating food supplies. Assume that the number of foxes, f(t), is given by f(t) = 300 + 200 sin t where t is time in years after a certain date. a. Store the equation for f(t) as y1 in your grapher, a

Calculus: Concepts and Applications 2
For Problems 1332, state whether the series converges. Justify your answer.

Calculus: Concepts and Applications 2
For Problems 120, a. Explain from the graph of the integrand whether the integral might converge. b. If the integral might converge, find out whether or not it does, and if so, the limit to which it converges

Calculus: Concepts and Applications 2
a. What is the physical meaning of the derivative of a function? What is the graphical meaning? b. For the function in Figure 1-6a, explain how f(x) is changing (increasing or decreasing, quickly or slowly) when x equals 4, 1, 3, and 5. 4 1 3 5 x f(x) Figure 1-6a c. If f(x) = 5x, find the average rat

Calculus: Concepts and Applications 2
Hot Tub Problem: Figure 7-3k shows a cylindrical hot tub 8 ft in diameter and 4 ft deep. At time t = 0 min, the drain is opened and water flows out. The rate at which it flows is proportional to the square root of the depth, y, in feet. Because the tub has vertical sides, the rate is also proportiona

Calculus: Concepts and Applications 2
Tugboat Problem: A tugboat moves a ship up to the dock by pushing its stern at a rate of 3 m/s (Figure 4-9f). The ship is 200 m long. Its bow remains in contact with the dock and its stern remains in contact with the pier. At what rate is the bow moving along the dock when the stern is 120 m from the

Calculus: Concepts and Applications 2
Base Runner Problem: Milt Famey hits a line drive to center field. As he rounds second base, he heads directly for third, running at 20 ft/s (Figure 4-9e). Write an equation expressing the rate of change of his distance from home plate as a function of his displacement from third base. Plot the graph

Calculus: Concepts and Applications 2
Nitrogen-17 Problem: When a water-cooled nuclear power plant is in operation, oxygen in the water is transmuted to nitrogen-17 (Figure 7-2d). After the reactor is shut down, the radiation from the nitrogen-17 decreases in such a way that the rate of change in the radiation level is directly proportio

Calculus: Concepts and Applications 2
Ramjet Problem: A ramjet (Figure 7-7a) is a relatively simple jet engine. The faster the plane goes, the more air is rammed into the engine and the more power the engine generates Figure 7-7a a. Assume that the rate at which the planes speed changes is directly proportional to its speed. Write a diff

Calculus: Concepts and Applications 2
Speeding Piston Project: A car engines crankshaft is turning 3000 revolutions per minute (rpm). As the crankshaft turns in the xy-plane, the piston moves up and down inside the cylinder (Figure 4-10f). The radius of the crankshaft is 6 cm. The connecting rod is 20 cm long and fastens to a point 8 cm

Calculus: Concepts and Applications 2
Ellipse Problem: Recall that the area of an ellipse is A = ab, where a and b are the lengths of the semiaxes (Figure 4-9d). Suppose that an ellipse is changing size but always keeps the same proportions, a = 2b. At what rate is the length of the major axis changing when b = 12 cm and the area is decr

Calculus: Concepts and Applications 2
Pipeline Problem: Earl Wells owns an oil lease. A new well 300 m from the road is to be connected to storage tanks 1000 m down the road from the well (Figure 10-5g). Building pipeline across the field costs $50 per meter, while building it along the road costs only $40 per meter. How should the pipel