Consider the following problem. Find the distance traveled in 18 seconds by an object traveling at a constant velocity of 20 feet per second. Decide whether the problem can be solved using precalculus, or whether calculus is required. 0 The problem can be solved using precalculus. O The problem requires calculus to be solved. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. ft Consider the function f(x) = vx and the point P(4,2) on the graph f. (a) Graph f and the secant lines passing through the point P(4, 2) and Q(x, f(x)) for x-values of 3, 5, and 7. 107 No -10 6 2 10 -10 8 6 202 4 6 8 10 -2- N O -103 O -10- 10 107 IN -10 8 6 4 2 8 -10 8 6 4 20 2 10 -2- -2 4 -6- -6- 8- -8- O -10- O -10 (b) Find the slope of each secant line. (Round your answers to three decimal places.) (line passing through Q(3, f(x))) (line passing through Q(5, f(x))) (line passing through Q(7, f(x))) (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(4,2). Describe how to improve your approximation of the slope. Choose secant lines that are nearly horizontal. O Choose secant lines that are nearly vertical. O Define the secant lines with points farther away from P. O Define the secant lines with points closer to P.Consider the figures below. (1) (2) 5- 5 - 4 4 3. 3 y 2- 2- 1- 1- Use the rectangles in each graph to approximate the area of the region bounded by y = 5/x, y = 0, x = 1, and x = 5. (Round your answers to three decimal places.) figure (1) figure (2) Describe how you could continue this process to obtain a more accurate approximation of the area. O Continually increase the height of all rectangles. O Continually decrease the height of all rectangles. O Continually decrease the number of rectangles. O Continually increase the number of rectangles