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Finding an Equation of a Tangent Line In Exercises 47-54, find an equation of the tangent line to the graph of the function at the given point. Then use a graphing utility to graph the function and the tangent line in the same viewing window. See Example 5.
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Chapter 2 Solutions
Bundle: Calculus: An Applied Approach, Brief, Loose-leaf Version, 10th + WebAssign Printed Access Card for Larson's Calculus: An Applied Approach, 10th Edition, Single-Term
- The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, and 14 inches, respectively. A cyclist pedals at a rate of 1 revolution per second. (a) find the speed of the bicycle in feet per second and miles per hour (b) Use your result from part (a) to write a function for the distance d (in miles) a cyclist travels in terms of the number n of revolutions of the pedal sprocket (c) write a function for the distance d (in miles) a cyclist travels in terms of the time t (in seconds)arrow_forwardplease help with math calculus application of derivatives functionarrow_forwardDistance between cars At noon, car A is 10 feet to the right and 20 feet ahead of car B, as shown in the figure. If car A continues at 88 ft/sec (or 60 mi/hr) while car B continues at 66 f/sec (or 45 mi/hr), express the distance d between the cars as a function of t, where t denotes the number of sec- onds after noon. Exercise 78arrow_forward
- Equation of a tangent line Let f(x) = -16x 2 + 96x (the position function examined in Section 2.1) and consider the point P(1, 80) on the curve. a. Find the slope of the line tangent to the graph of f at P. b. Find an equation of the tangent line in part (a).arrow_forwardSketch by hand the graphs of the functions in parts (a), (b), (c) and answer question in part (d)arrow_forwardCalculus Derivatives of inverse trig functionsarrow_forward
- The graph of fis shown in the figure. Sketch a graph of the derivative ofrf. O a) -2. b)arrow_forwardHorizontal Tangent line. Determine the points (if any) at which the function has a horizontal tangent line.arrow_forwardTide height as a function of time resembles a sinusoidal function during the time between low and high tide. At one such location on another planet with water, the tide has a high of 12.7 feet at 2 am and then the next low is -0.8 feet at 11 am (9 hours later). Find a formula for a sinusoidal function H(t) that gives the height tt hours after midnight.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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