Concept explainers
Equations of tangent lines by definition (2)
- a. Use definition (2) (p. 129) to find the slope of the line tangent to the graph of f at P.
- b. Determine an equation of the tangent line at P.
23.
Trending nowThis is a popular solution!
Chapter 3 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Precalculus
Glencoe Math Accelerated, Student Edition
University Calculus: Early Transcendentals (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Tangent Line to a Circle Find an equation for the line tangent to the circle x2+y2=25 at the point (3,4).see the figure. At what other point on the circle will a tangent line be parallel to the tangent line in part a?arrow_forwardAverage Rate of change A fucntion f is given. (a) Find the average rate of change of f between x=0 and x=0 , and the average rate of change of f between x=15 and x=50 .(b) Were the two average rates of change that you found in part (a) the same? (c) Is the function linear? If so, what is its rate of change? f(x)=83xarrow_forwardMannings Equation Hydrologists sometimes use Mannings equation to calculate the velocity v in feet per second, of water flowing through a pipe. The velocity depends on the hydraulic radius R in feet, which is one-quarter of the diameter of the pipe when the pipe if flowing full; the slope S of the pipe, which gives vertical drop in feet for each horizontal foot; and the roughness coefficient n, which depends on the material of which the pipe is made. The relationship is given by v=1.486nR2/3S1/2 For a certain brass pipe, the roughness coefficient has been measured to be n=0.012. The pipe has a diameter of 3 feet and a slope of 0.2 foot per foot. That is, the pipe drops 0.2 foot for each horizontal foot. If the pipe is flowing full, find the hydraulic radius of the pipe, and find the velocity of the water flowing through the pipe.arrow_forward
- Radius of a Shock Wave An explosion produces a spherical shock wave whose radius R expands rapidly. The rate of expansion depends on the energy E of the explosion and the elapsed time t since the explosion. For many explosions, the relation is approximated closely by R=4.16E0.2t0.4. Here R is the radius in centimeters, E is the energy in ergs, and t is the elapsed time in seconds. The relation is valid only for very brief periods of time, perhaps a second or so in duration. a. An explosion of 50 pounds of TNT produces an energy of about 1015 ergs. See Figure 2.71. How long is required for the shock wave to reach a point 40 meters 4000 centimeters away? b. A nuclear explosion releases much more energy than conventional explosions. A small nuclear device of yield 1 kiloton releases approximately 91020 ergs. How long would it take for the shock wave from such an explosion to reach a point 40 meters away? c. The shock wave from a certain explosion reaches a point 50 meters away in 1.2 seconds. How much energy was released by the explosion? The values of E in parts a and b may help you set an appropriate window. Note: In 1947, the government released film of the first nuclear explosion in 1945, but the yield of the explosion remained classified. Sir Geoffrey Taylor used the film to determine the rate of expansion of the shock wave and so was able to publish a scientific paper concluding correctly that the yield was in the 20-kiloton range.arrow_forwardFind the slope of the line shown in the graph.arrow_forwardThe Doppler Effect As a train moves toward an observer (see the figure), the pitch of its whistle sounds higher to the observer than it would if the train were at rest, because the crests Of the sound waves are closer together. 'This phenomenon is called the Doppler effect. The observed pitch P is a function of the speed v of the train and is given by P(v)=poSoSov where PO is the actual pitch of the whistle at the source and So = 332 rn/s is the speed of sound in air. Suppose that a train has a whistle pitched at Po = 440 Hz. the function y = P(v) using a graphing device. How can the vertical asymptote of this function be interpreted physically?arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning