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In Problems 27–32, graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated
30.
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- 7. The region D above lies between the two red lines and 2 -². It can be described in two 1 the red parabola y: = ways. 1. If we visualize the region having "top" and "bottom" boundaries, express each as functions of x and provide the interval of x-values that covers the entire region. "top" boundary g₂(x) = "bottom" boundary g₁(x): interval of a values that covers the region = 2. If we visualize the region having "right" and "left" boundaries, express each as functions of y and provide the interval of y-values that covers the entire region. "right" boundary f2(y): "left" boundary fi(y) = interval of y values that covers the region =arrow_forward11) A cam is designed with a lens that is described as the following area between two curves: а+ +b. Units are in cm. The red top curve is f(x) = x3 - 2x2-x+2 The blue bottom curve is g(x) = x² - 1 Find the area in cm²arrow_forward5.1: 9) Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t=0 and t=x for the graph below. Evaluate A(x)for x=1, 2, 3, and 4. A(1)=? A(2)=? A(3)=? A(4)=?arrow_forward
- 2x. 5. Find the area of the region bounded by the curves x²y = 2, x²y = 3, y = x and y =arrow_forward7. The region D above can be describe in two ways. 1. If we visualize the region having "top" and "bottom" boundaries, express each as functions of a and provide the interval of -values that covers the entire region. "top" boundary g2 (x) - "bottom" boundary 9₁(x) = interval of values that covers the region 2. If we visualize the region having "right" and "left" boundaries, express each as functions of y and provide the interval of y-values that covers the entire region. "right" boundary f2(y) = "left" boundary f₁(y) = interval of y values that covers the regionarrow_forwardQ.5 a) The function describing the marginal profit from producing and selling a product is MP = -3x + 500 Where x equals the number of units and MP is the marginal profit measured in dollars. When 200 units are produced and sold, total profit equals $15.00. Determine the total profit function. b) Given f(x) = xr² and g(x) = 3x + 8, for x 2 0 detemine the area bounded on three sides by the two functions are the y-axisarrow_forward
- 2a. 2b. 2c.arrow_forward6. Area of a Region between Two Curves. a. Determine the area of the region bounded by f(x) = (x − 1)³ and g(x) = x − 1. b. Determine value of the area of the region bounded by f(x) = -x² + 9 10 and g(x) = 2/1/2 c. Determine value of the area of the region bounded by f(y) = y² + 1, g(y) = 0, y = 1, y = 3arrow_forwardThe region D above lies between the two red lines and the red parabola y = two ways. 1. If we visualize the region having "top" and "bottom" boundaries, express each as functions of x and provide the interval of x-values that covers the entire region. "top" boundary 92(x) = "bottom" boundary 9₁(x) = interval of values that covers the region "left" boundary f₁(y) 2. If we visualize the region having "right" and "left" boundaries, express each as functions of y and provide the interval of y-values that covers the entire region. "right" boundary f₂(y) = = 0 interval of y values that covers the region MI 3 21x². - x². It can be described in =arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage