Concept explainers
Evaluating a Function In Exercises 1-10, evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = cos 2x
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Calculus
- A lighthouse (L) is located on a small island 3800 meters from the nearest point P on a straight shoreline. Its light makes 1 revolutions per minute. Let A be the point where the beam of light strikes the shore and x the angle ALP. Write the distance D from A to P as a function of x. D( x ) = How fast is the beam of light moving along the shoreline when it is 550 meters from P? dD meters per minute dt symbolic formatting helparrow_forwardQuestion: How do you determine if a function f (x) has an inverse on an interval (a, b)?arrow_forwardConsider the function. f(x) = x7 − 1 (a) Find the inverse function of f. f −1(x) = (b) describe the relationship between the graphs.arrow_forward
- An equation (formula) for this function.arrow_forwardUse a graphing utility to graph the function h(t) = 2/(t − 3), and use the Horizontal Line Test to determine whether the function has an inverse function.arrow_forwardAn airplane is flying at a speed of 450 mi/h at an altitude of one mile. The plane passes directly above a radar station at time t = 0. 1 mi (a) Express the distance s (in miles) between the plane and the radar station as a function of the horizontal distance d (in miles) that the plane has flown. s(d) = (b) Express d (in miles) as a function of the time t (in hours) that the plane has flown. d(t) = (c) Use composition to express s as a function of t. s(t) =arrow_forward
- Tutorial Exercise Determine where the function is concave upward and where it is concave downward. (Enter your answer using interval notation. If an answer does not exist, enter DNE.) f(x) = 3x4 - 36x3 + x – 4 Part 1 of 6 We use the ---Select--- Notice that the domain of f is (Enter your answer using interval notation.) First, find the first and second derivatives of f(x) = 3x – 36x3 + x – 4. f'(x) = f"(x) = Submit Skip (you cannot come back)arrow_forwardThe radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling 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 time t (in seconds). Compare this function with the function from part (b).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage