1. Sketch the graph of the polar equation r = 8 cos 20. Use animation command...
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1. Sketch the graph of the polar equation r = 8 cos 20. Use animation command to get a feel for the motion of the particle as it traces out the curve. Find the area it encloses. 20-x 2. Use MATLAB to sketch a butterfly curve re-2 cos 40+ sin Sketch the polar 24 curve in the interval 0 ≤0<2. Use the result to explain the name of this curve. What happens when you extend the interval of 0 to [0,4]? 3. Use MATLAB to find the volume of the solid obtained by rotating about the x-axis the region under the curves y=1-x.y=0. Sketch the region and the resulting solid. 1111 3'5'7'9" 4. Graph the first 60 terms of the sequence 1.- From the graph conjecture whether or not the sequences converge and if it converges, conjecture what the limit is. Use calculus to find the limit. Is the sequence increasing or decreasing? Explain. 5. Use MATLAB to find the area of the region bounded by the given function and the x-axis. Assume is continuous and positive on the interval[1,4]. Plot the curve and show the region (area to be evaluated). Then compute the exact area x +4 f(x)= X 1. Sketch the graph of the polar equation r = 8 cos 20. Use animation command to get a feel for the motion of the particle as it traces out the curve. Find the area it encloses. 20-x 2. Use MATLAB to sketch a butterfly curve re-2 cos 40+ sin Sketch the polar 24 curve in the interval 0 ≤0<2. Use the result to explain the name of this curve. What happens when you extend the interval of 0 to [0,4]? 3. Use MATLAB to find the volume of the solid obtained by rotating about the x-axis the region under the curves y=1-x.y=0. Sketch the region and the resulting solid. 1111 3'5'7'9" 4. Graph the first 60 terms of the sequence 1.- From the graph conjecture whether or not the sequences converge and if it converges, conjecture what the limit is. Use calculus to find the limit. Is the sequence increasing or decreasing? Explain. 5. Use MATLAB to find the area of the region bounded by the given function and the x-axis. Assume is continuous and positive on the interval[1,4]. Plot the curve and show the region (area to be evaluated). Then compute the exact area x +4 f(x)= X
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