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6. The curve y = ex, the x-axis, the y-axis and the vertical line x =...
7. Find the rectangle of largest area that can be inscribed under f(x)-9-x and above theX-axis. radvea ans)
7. Find the rectangle of largest area that can be inscribed under f(x)-9-x and above theX-axis. radvea ans)
2. (a) Find the area of the region bounded by the parabolas y 6z - 2 and y 22 (b) (Optional) Find the area of the region between the curves y2 and y - 22".. over the interval [0,2. 2 36 3. (Review) Evaluate the limit lim 4. (Review) A rectangle has its base on the z-axis and its two upper vertices on the curve y 5-x4. What is the largest area the rectangle can have?
2. (a) Find the...
Please do both
3. A rectangle has its base on the x-axis and it upper two vertices on the parabola y = 12 - x? What dimensions will maximize the area of the rectangle? 4. What are the dimensions of the right circular cylinder of greatest volume that can be inscribed in a sphere with radius 8 inches? OE (S! R4 135=61 rta 64 - 4
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 11-2P. What are the dimensions of such a rectangle with the greatest possible area? Width- Preview Height- Preview
8. (8 points) Use calculus to find the dimensions of the rectangle of largest area that can be inscribed in the region bounded by x+y=1, and the positive r and y axes. 0.8 0.6 0.4 x + y = 1 0.2 0.5
Consider the area bound by the line y- xì and y x? where 0 SxS1. Find the volume line of rotation when this area is rotated about a) the x-axis, b) the y-axis, c) the line
Consider the area bound by the line y- xì and y x? where 0 SxS1. Find the volume line of rotation when this area is rotated about a) the x-axis, b) the y-axis, c) the line
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = r. Find the area of this region. YA y = 1 y= x 1 * Area =
1. Use the method of cylindrical shells to find the volume of the following solids rotation (i) Spin the region bound by y -Vx,y 0, x-1 around the y-axis; (ii) Twist the area bound by x -1+(y-2)2 andx- 2 about the x-axis; (iii) Rotate the region between y - x2 and y -6x-2x2 around the y-axis; (iv) Twirl the space between y V and x 2y about the line x 5 2. Use both methods discussed in class to compute...
Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ellipse = 1 with sides parallel to the coordinate axes Let length be the dimension parallel to the x-axis and let width be the dimension parallel to the y-acis.