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Newton's Method and Four Rectangles and the Right Endpoint Method

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Question #1. Find the positive root of the equation cos(x) = sin(x) + x^4 using Newton's method (Do only 3 iterations).

Question #2. The acceleration of object is given by the following equation: a(t) = cost(t) - 3t^2 + e^t. We also know that v(0) = 8cm/sec and s(0) = 32cm. Find the position of the object after 3 seconds.

Question #4. Find the most general anti-derivative of the following functions:

i. h(theta) = sin(theta)/cos^2(theta)

Qustion #5. Find the area under the graph of y = the square root of (x + 8) from x = 1 to x=3 using:

i. 4 rectangles and the right endpoint method

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Problem #1
Let , then .
Now we use Newton's method to find a positive ...

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Newton's Method and Four Rectangles and the Right Endpoint Method are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.