Advanced Placement Calculus 2016 Graphical Numerical Algebraic Fifth Edition Student Edition
5th Edition
ISBN: 9780133311617
Author: Prentice Hall
Publisher: Prentice Hall
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Find The Derivative
A cardiac monitor is used to measure the heart rate of a patient after surgery. It complies the number of heartbeats after t minutes. When data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute.
t (min)
Heartbeats
(b) t-38 and t - 42
(c) t-40 and t - 42
36
(d) t-42 and t-44
38
2,503 2,639
40
2,773
The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with the given values of t. (Round your answers to one decimal place.)
(a) t-36 and t-42
42
44
2,903 3,033
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- Explain your understanding of the connection between the derivative of a constant and the slope of the tangent of a function. Use a diagram in your solutionarrow_forwardPls answer asaparrow_forward4 2+x (Use decimal notation. Give your answer to three decimal places.) Estimate the slope of the tangent line of the function y(x) slope of the tangent line = = at x = 1.arrow_forward
- ACTIVITY 3: Think More! 1. Find the equations of the two tangent lines to f(x) = x2 that pass through the point (-1,3), a point not on the graph of f. (Hint: Sketch the scenario first.) **Use GeoGebra or Desmos graphing calculator for easier sketching of graphs.arrow_forwardungent Function *12. In Exercise #2 you were asked to calculate the slope of the terminal ray of the angle when you knew that the ray began at the origin and passed through a point on the circle. For example, if the terminal ray passed through the point (0.1736, 0.9848) then the slope is calculated as follows. 0.9848-0 m = 0.1736-0 0.9848 0.1736 5.673 a. Suppose you know that an angle measures 0 radians using a circle with a radius of 5 units. How can you find the point (x, y) on the circle through which the terminal ray passes? b. Using your answer to part (a), complete the following statement by writing tan(0) in terms of cos(0) and sin(0). (In other words, when we know the value of cos(0) and sin(0), how can we determine the value of tan(0)?) tan(0) =arrow_forward
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