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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
29.
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- Find two nonnegative number x and y for which x+3y=30, such that x2y is maximized.arrow_forward.Find extrema for a function y=f(x)%3D2X² - 8x on an interval [0, 6].arrow_forward7. 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_forward
- 21. Let D denote the region between the parabola y = 8 - x² and the line y = x + 2. Compute ff 2x + y dA.arrow_forward5. Find the area bounded by the parabolas y2=4x and y2+12x=36 6. Find the area bounded by the curve y=4x-x2and the lines x=-2 and y=4 7. Find the area bounded by the functions y=3x-x3and line y=2 8. Find the area in the first quadrant bounded by the curve x2y=a3and the lines x=2a, y=4a, and the axes.arrow_forward26. A rectangle has one vertex on the line y = 10 – x, x > 0, another at the origin, one on the positive x-axis, and one on the positive y-axis. Express the area A of the rectangle as a function of x. Find the largest area A that can be enclosed by the rectangle.arrow_forward
- 7. 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_forward5. Find the area of the region between the graphs of f(x) = x3 – 2x2 + x – 1 and g(x) = -x² + 3x – 1. - 6. Find the area of the region enclosed by the graphs of the functions y = 8 – x2, y = 7x, and y = 2x in the first quadrant.arrow_forward4. Are the following functions cubic splines? a. f(x) - x - 2x + 3, 0 sxs1, = 2x - 3x2 + x + 2, 1sxs2. b. f(x) = 5x - 3x + 1,0 sxs1, - 2x + 6x? - 9x + 4, 1sxs2.arrow_forward
- 12. x = 5 – 5t and y = -t + 3 for 1arrow_forwardConsider the following. x3 √6-x y = y = 0 X = 5 (a) Use a graphing utility to graph the region bounded by the graphs of the equations. 12 6- 10- 8- у 6 4 2 12+ 10 8 y 6- 4 2 2 3 X 4 니 2 3 4 X 6 5 4- y 3 2- 1- 12 10- 8- y 6- 4- 2 0.5 1 1.5 2 X 2.5 3 3.5 ..(b.). Use the integration capabilities of the graphing utility to approximate the area to four decimal places. 90.3545arrow_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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