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Given is the surface enclosed by the x-axis, the y-axis, the function f(x)=2x-2 and its tangent...
Exercise 3 Given is the following partial differential equation: Show that w(x, y, z)= sin(52) is...
Exercise 3 Given is the following partial differential equation: Show that w(x, y, z)= sin(52) is a solution of this partial differential equation. Exercise 4 Given is a three-dimensional volume enclosed by the planes y=0,2 = 0, y = and z=a-x+y, with a > 0 a constant. -x (4a) Make a three-dimensional sketch of this volume. Clearly indicate all characteristic features. (4b) Give an integral, with integration boundaries, that can be used for calculating the volume of the object. (4c)...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2.2,6) b) The parametric equations of the normal line at the point (2, 2, 6) c) The outward unit normal vector to the surface at the point (2, 2,6) d) Sketch the surface and the outward unit normal vector at the point (2, 2,6). 1.
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the...
Find the volume generated by revolving about the x-axis, the region enclosed by y=x^2+1 and 3x−2y=−4 Be sure to draw the region in the x-y plane, label the axis of revolution, state your method (disc...
Find the volume generated by revolving about the x-axis, the region enclosed by y=x^2+1 and 3x−2y=−4 Be sure to draw the region in the x-y plane, label the axis of revolution, state your method (disc or shell), draw a rectangle to be rotated, label the thickness (dx or dy), state the integral, and sketch the resulting 3D shape. State the volume exactly. show all work please.
10. Neatly sketch the region enclosed by the graph of y = Vx, the x-axis, and...
10. Neatly sketch the region enclosed by the graph of y = Vx, the x-axis, and x = 3. Find the volume of the solid generated by revolving this region around the axes given below. (Use the method of your choice.) Set up an INTEGRAL and then evaluate it using your calculator. a.) About the x-axis b.) About the y-axis c.) About the line x = 4
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g ...
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g represents the direction in which g increases the fastest. Notice that this is the direction in the xy plane corresponding to the steepest slope up the surface, with magnitude equal to the slope in that direction. 1. At the point (2, π), find the gradient, and explain what it means. 2. Use it to construct a vector in the tangent...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
Calculate the finite area enclosed by y = x ^ {^ {3}} and its tangent line...
Calculate the finite area enclosed by y = x ^ {^ {3}} and its tangent line at x = \ frac {-1} {2}.
Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis....
Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method, and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution Find the moment of inertia of the solid of revolution with respect to the x-axis. d)
Math232 2 Consider...
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If...
true or false
is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
Instructions: Show all your work for FULL credit. Calculators are NOL final answer. Neatness is highly appreciated. 1. A region R, bounded by y 2x, y 6-x, and x-axis, is rotated around the y-axis. Sk...
Instructions: Show all your work for FULL credit. Calculators are NOL final answer. Neatness is highly appreciated. 1. A region R, bounded by y 2x, y 6-x, and x-axis, is rotated around the y-axis. Sketch the region R, in the box a) 15 strip/slice you will use to find the volume of the solid of revolution. b) Write the definite integral that gives a X the volume of the solid of revolution. (DO NOT evaluate the integral.) Find the circumference...
Exercise 3 Given is the following partial differential equation: Show that w(x, y, z)= sin(52) is a solution of this partial differential equation. Exercise 4 Given is a three-dimensional volume enclosed by the planes y=0,2 = 0, y = and z=a-x+y, with a > 0 a constant. -x (4a) Make a three-dimensional sketch of this volume. Clearly indicate all characteristic features. (4b) Give an integral, with integration boundaries, that can be used for calculating the volume of the object. (4c)...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2.2,6) b) The parametric equations of the normal line at the point (2, 2, 6) c) The outward unit normal vector to the surface at the point (2, 2,6) d) Sketch the surface and the outward unit normal vector at the point (2, 2,6). 1.
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the...
10. Neatly sketch the region enclosed by the graph of y = Vx, the x-axis, and x = 3. Find the volume of the solid generated by revolving this region around the axes given below. (Use the method of your choice.) Set up an INTEGRAL and then evaluate it using your calculator. a.) About the x-axis b.) About the y-axis c.) About the line x = 4
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method, and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution Find the moment of inertia of the solid of revolution with respect to the x-axis. d)
Math232 2 Consider...
true or false
is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
Instructions: Show all your work for FULL credit. Calculators are NOL final answer. Neatness is highly appreciated. 1. A region R, bounded by y 2x, y 6-x, and x-axis, is rotated around the y-axis. Sketch the region R, in the box a) 15 strip/slice you will use to find the volume of the solid of revolution. b) Write the definite integral that gives a X the volume of the solid of revolution. (DO NOT evaluate the integral.) Find the circumference...
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