
Concept explainers
Making a Function Differentiable In Exercises 117 and 118, find a and b such that f is differentiable everywhere.

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Chapter 3 Solutions
Calculus: Early Transcendental Functions
- (5) (10 points) Let D be the parallelogram in the xy-plane with vertices (0, 0), (1, 1), (1, 1), (0, -2). Let f(x,y) = xy/2. Use the linear change of variables T(u, v)=(u,u2v) = (x, y) 1 to calculate the integral f(x,y) dA= 0 ↓ The domain of T is a rectangle R. What is R? |ǝ(x, y) du dv. |ð(u, v)|arrow_forward2 Anot ined sove in peaper PV+96252 Q3// Find the volume of the region between the cylinder z = y2 and the xy- plane that is bounded by the planes x=1, x=2,y=-2,andy=2. vertical rect a Q4// Draw and Evaluate Soxy-2sin (ny2)dydx D Lake tarrow_forwardDetermine whether the Law of Sines or the Law of Cosines can be used to find another measure of the triangle. B 13 cm 97° Law of Sines Law of Cosines A 43° Then solve the triangle. (Round your answers to two decimal places.) b = x C = A = 40.00arrow_forward
- Find the missing values by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by c and d. Round your answers to two decimal places.) a 29 b 39 d Ꮎ 126° a Ꮎ b darrow_forwardA retractable awning above a patio lowers at an angle of 50° from the exterior wall at a height of y = 11 feet above the ground. No direct sunlight is to enter the door when the angle of elevation of the sun is greater than 70° (see figure). What is the length x of the awning? (Round your answer to two decimal places.) x = ft 7507 Suns rays 70°arrow_forwardhelp and show work plsarrow_forward
- Two ships leave a port at 9 a.m. One travels at a bearing of N 53° W at 10 miles per hour, and the other travels at a bearing of S 67° W at 14 miles per hour. Approximate how far apart they are at noon that day. (Round your answer to one decimal place.) miarrow_forwardIn the triangle below, x = 7. Use the Law of Cosines to solve the triangle. A = B = C = 12 cm 18 cm B x cm ° о °arrow_forwardA triangular parcel of ground has sides of length 750 feet, 650 feet, and 535 feet. Find the measure of the largest angle. (Round your answer to one decimal place.)arrow_forward
- A boat is sailing due east parallel to the shoreline at a speed of 10 miles per hour. At a given time, the bearing to a lighthouse is S 70° E, and 15 minutes later, the bearing is S 63° E (see figure). The lighthouse is located at the shoreline. Find the distance d from the boat to the shoreline. (Round your answer to one decimal place.) x mi N 63° WE 70° Sarrow_forwardA 120-foot vertical tower is to be erected on the side of a hill that makes a 6° angle with the horizontal. Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower (see figure). (Note that x = 120 in the figure. Round your answers to one decimal place.) shorter wire longer wire x ft ft ft XXXX -75 ft -75 ftarrow_forwardhelp with workarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage