Q. 100 (a) Graph f(x)=2cosx2+3聽and聽g(... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 100 (page 466)

(a) Graph $f (x) = 2 \cos \frac{x}{2} + 3 and g (x) = 4$ on the same Cartesian plane for the interval $[0, 4 蟺] .$
(b) Solve $f (x) = g (x)$ on the interval $[0, 4 蟺]$ and label the points of intersection on the graph drawn in part (a).
(c) Solve $f (x) < g (x)$ on the interval $[0, 4 蟺] .$
(d) Shade the region bounded by $f (x) = 2 \cos \frac{x}{2} + 3 and g (x) = 4$ between the two points found in part (b) on the graph drawn in part (a).

Short Answer

Expert verified

Part a. The graph of $f (x) = 2 \cos \frac{x}{2} + 3 and g (x) = 4$ on the same cartesian plane for the interval $[0, 4 蟺]$ is

Part b. The solution of $f (x) = g (x) on the interval [0, 4 蟺]$ is $\frac{2 蟺}{3}, \frac{10 蟺}{3}$ and the points on the graph is

Part c. The solution of $f (x) < g (x) on the interval [0, 4 蟺]$ is $\frac{2 蟺}{3} < x < \frac{10 蟺}{3} .$

Part d. The shaded region bounded by $f (x) = 2 \cos \frac{x}{2} + 3 and g (x) = 4$ between the two points found in part (b) on the graph drawn in part (a) is

Step by step solution

Part (a) Step 1. Given Information

The given functions are $f (x) = 2 \cos \frac{x}{2} + 3 and g (x) = 4 .$

We have to graph the given functions on the same cartesian plane for the interval $[0, 4 蟺] .$

Part (a) Step 2. Sketch the graph

The graph of $f (x) = 2 \cos \frac{x}{2} + 3 and g (x) = 4$ on the same cartesian plane for the interval $[0, 4 蟺]$ is

Part (b) Step 1. Solving

We have to solve $f (x) = g (x), 0 鈮� x 鈮� 4 蟺 .$

$f (x) = g (x) 2 \cos \frac{x}{2} + 3 = 4 2 \cos \frac{x}{2} = 1 \cos \frac{x}{2} = \frac{1}{2} \frac{x}{2} = \frac{蟺}{3}, \frac{5 蟺}{3} x = \frac{2 蟺}{3}, \frac{10 蟺}{3}$

Part (c) Step 1. Solving

We have to solve $f (x) < g (x) on the interval [0, 4 蟺] .$

$f (x) < g (x) 2 \cos \frac{x}{2} + 3 < 4 \cos \frac{x}{2} < \frac{1}{2} \frac{蟺}{3} < \frac{x}{2} < \frac{5 蟺}{3} \frac{2 蟺}{3} < x < \frac{10 蟺}{3}$

Part (d) Step 1. Shading the region

The shaded region bounded by $f (x) = 2 \cos \frac{x}{2} + 3 and g (x) = 4$ between the two points found in part (b) on the graph drawn in part (a) is

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Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Sketch the graph

Part (b) Step 1. Solving

Part (c) Step 1. Solving

Part (d) Step 1. Shading the region

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