Family of curves In each exercise, obtain the differential equation of the family of plane curves described. 1. Family of lines passing through (-1,1) 2. All circles of radius 1 and centers on the line y = x 3. Straight lines with slope and y-intercept equai 4. Circles with center on the x-axis 5. sine waves with a period of 2m and a phase shift of 0°

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A: Differentiate two times

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A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

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A: For a negative exponent, we will use reciprocal first.

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A:

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A: Explanation of the answer is as follows

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A: Use the formula and evaluate.

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A:

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A:

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A:

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Q: 6. Evaluate. (-125) } a. 25 b. -25 C. 5 d. -5

A: