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sin 4x Does it exist? '. 1. Calculate lim 2. Find lim x-2 x-2 x-2 3. Find the asymptotes of - and plot them as dashed lines with the ..2 x² – 3x function. Cos 4. Compute lim 0→π/21+ sin 0 1 5. Consider the function f(x) = 3x² +1 a) What are the first and second derivatives? b) What are the critical points for this function? c) What is f" evaluated at these critical points? d) Are there any local minima or maxima? Plot the function and show them on the graph. 6. Use MATLAB to show that y = 2 sin t-3 cos t does not satisfy y" - 11y = -4 cos 6t. 7. Find a solution of dx/dt = -2x + 8 and plot for constants C1 = 1,2,...5 on the same graph. 8. Find a solution of y" - y' -2y = 2t, y(0) = 0, y' (0) = 0. 9. Solve the system x" + x = 0, p'+p+x=0, x (0) = 4, x' (0) = p(0) = 0. 10. Solve the system x" + 2x' + x = 0, p' = x, x (0) = 1, x' (0) = p(0) = 0 and generate a phase portrait. x 0 X

sin 4x Does it exist? '. 1. Calculate lim 2. Find lim x-2 x-2 x-2 3. Find the asymptotes of - and plot them as dashed lines with the ..2 x² – 3x function. Cos 4. Compute lim 0→π/21+ sin 0 1 5. Consider the function f(x) = 3x² +1 a) What are the first and second derivatives? b) What are the critical points for this function? c) What is f" evaluated at these critical points? d) Are there any local minima or maxima? Plot the function and show them on the graph. 6. Use MATLAB to show that y = 2 sin t-3 cos t does not satisfy y" - 11y = -4 cos 6t. 7. Find a solution of dx/dt = -2x + 8 and plot for constants C1 = 1,2,...5 on the same graph. 8. Find a solution of y" - y' -2y = 2t, y(0) = 0, y' (0) = 0. 9. Solve the system x" + x = 0, p'+p+x=0, x (0) = 4, x' (0) = p(0) = 0. 10. Solve the system x" + 2x' + x = 0, p' = x, x (0) = 1, x' (0) = p(0) = 0 and generate a phase portrait. x 0 X

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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sin 4x Does it exist? '. 1. Calculate lim 2. Find lim x-2 x-2 x-2 3. Find the asymptotes of - and plot them as dashed lines with the ..2 x² – 3x function. Cos 4. Compute lim 0→π/21+ sin 0 1 5. Consider the function f(x) = 3x² +1 a) What are the first and second derivatives? b) What are the critical points for this function? c) What is f" evaluated at these critical points? d) Are there any local minima or maxima? Plot the function and show them on the graph. 6. Use MATLAB to show that y = 2 sin t-3 cos t does not satisfy y" - 11y = -4 cos 6t. 7. Find a solution of dx/dt = -2x + 8 and plot for constants C1 = 1,2,...5 on the same graph. 8. Find a solution of y" - y' -2y = 2t, y(0) = 0, y' (0) = 0. 9. Solve the system x" + x = 0, p'+p+x=0, x (0) = 4, x' (0) = p(0) = 0. 10. Solve the system x" + 2x' + x = 0, p' = x, x (0) = 1, x' (0) = p(0) = 0 and generate a phase portrait. x 0 X
Transcribed Image Text:sin 4x Does it exist? '. 1. Calculate lim 2. Find lim x-2 x-2 x-2 3. Find the asymptotes of - and plot them as dashed lines with the ..2 x² – 3x function. Cos 4. Compute lim 0→π/21+ sin 0 1 5. Consider the function f(x) = 3x² +1 a) What are the first and second derivatives? b) What are the critical points for this function? c) What is f" evaluated at these critical points? d) Are there any local minima or maxima? Plot the function and show them on the graph. 6. Use MATLAB to show that y = 2 sin t-3 cos t does not satisfy y" - 11y = -4 cos 6t. 7. Find a solution of dx/dt = -2x + 8 and plot for constants C1 = 1,2,...5 on the same graph. 8. Find a solution of y" - y' -2y = 2t, y(0) = 0, y' (0) = 0. 9. Solve the system x" + x = 0, p'+p+x=0, x (0) = 4, x' (0) = p(0) = 0. 10. Solve the system x" + 2x' + x = 0, p' = x, x (0) = 1, x' (0) = p(0) = 0 and generate a phase portrait. x 0 X
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