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1a. Give two solutions to the equation y = Vx³ + 2x² – x +5. Make a rough sketch of the %3D graph, and label your solutions on your sketch. All solutions should be correct to three decimal places. 1b. Verify that your two solutions are approximately correct by plugging them into the equation. Show your work.

1a. Give two solutions to the equation y = Vx³ + 2x² – x +5. Make a rough sketch of the %3D graph, and label your solutions on your sketch. All solutions should be correct to three decimal places. 1b. Verify that your two solutions are approximately correct by plugging them into the equation. Show your work.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1a. Give two solutions to the equation y = Vx' + 2x² – x + 5. Make a rough sketch of the graph, and label your solutions on your sketch. All solutions should be correct to three decimal places. 1b. Verify that your two solutions are approximately correct by plugging them into the equation. Show your work. 2. Consider the following system of equations. x + 2y = 4 Зх — у %3D 2 -글x-4y %3D3 2a. Estimate all solutions to this system, rounding to three decimal places when needed. If there are no solutions, then write “No Solutions" and explain your reasoning. 2b. Remove the first equation from the system. What are the solutions now? If there are no solutions, then write "No Solutions" and explain your reasoning. 3. Your friend is in a calculus class, and they are trying to solve the following system of equations: Sy = x? – 6x + 8 - x² + 2x + 3 Your friend says there are four solutions: (2,0), (4,0), (–1,0), and (3,0). If your friend is correct, explain why they are correct. If your friend is incorrect, give the correct solution(s) to the system. As before, label your solutions on a rough sketch and write all solutions correct to three decimal places.
Transcribed Image Text:1a. Give two solutions to the equation y = Vx' + 2x² – x + 5. Make a rough sketch of the graph, and label your solutions on your sketch. All solutions should be correct to three decimal places. 1b. Verify that your two solutions are approximately correct by plugging them into the equation. Show your work. 2. Consider the following system of equations. x + 2y = 4 Зх — у %3D 2 -글x-4y %3D3 2a. Estimate all solutions to this system, rounding to three decimal places when needed. If there are no solutions, then write “No Solutions" and explain your reasoning. 2b. Remove the first equation from the system. What are the solutions now? If there are no solutions, then write "No Solutions" and explain your reasoning. 3. Your friend is in a calculus class, and they are trying to solve the following system of equations: Sy = x? – 6x + 8 - x² + 2x + 3 Your friend says there are four solutions: (2,0), (4,0), (–1,0), and (3,0). If your friend is correct, explain why they are correct. If your friend is incorrect, give the correct solution(s) to the system. As before, label your solutions on a rough sketch and write all solutions correct to three decimal places.
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