Consider the function f(x) = cos(2) in the interval [0,2]. Within the interval (0,2), the critical...

  

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Consider the function f(x) = cos(2) in the interval [0,2]. Within the interval (0,2), the critical points of f(x) are at r = 0.86 and z 3.426. Also, the critical points of f'(x) are at z 2.289 and 1= 5.087 (a) [1 point] Sketch the graph of f(x) in the interval (0, 2x]. Shadow the region bounded by the curve y = f(r) and the z-axis. (b) [2 points] Use the Fundamental Theorem of Calculus II to find the area of the shaded region in Part (a), i.e., S 12 cos(x)\dr. 4 (c) [1 point] Rotate the shaded region described in Part (a) around the z-axis to generate a solid. A cross-sectional region A(z) at a point z on the z-axis (the axis of rotation) is obtained by intersecting the solid with a plane perpendicular to the z-axis passing through r. Describe the shape of A(z) and determine the area of A(x). (d) [2 point] Evaluate A(x)dx. Consider the function f(x) = cos(2) in the interval [0,2]. Within the interval (0,2), the critical points of f(x) are at r = 0.86 and z 3.426. Also, the critical points of f'(x) are at z 2.289 and 1= 5.087 (a) [1 point] Sketch the graph of f(x) in the interval (0, 2x]. Shadow the region bounded by the curve y = f(r) and the z-axis. (b) [2 points] Use the Fundamental Theorem of Calculus II to find the area of the shaded region in Part (a), i.e., S 12 cos(x)\dr. 4 (c) [1 point] Rotate the shaded region described in Part (a) around the z-axis to generate a solid. A cross-sectional region A(z) at a point z on the z-axis (the axis of rotation) is obtained by intersecting the solid with a plane perpendicular to the z-axis passing through r. Describe the shape of A(z) and determine the area of A(x). (d) [2 point] Evaluate A(x)dx.