Let x1 = 1.5. Using Newton\'s Method, state the formula for X2 and then find X2.

Question

Let x1 = 1.5. Using Newton's Method, state the formula for X2 and then find X2. Show all of your work. Illustrate the procedure on the diagram below. State the formula for x3 and X4, and then find X3 and X4. Show all of your work. Illustrate the procedure on the diagram below. Do all of your calculated values for X2, X3 and X4 seem to be approaching the value of "c" where f(x) crosses the x-axis (i.e., the root)? What is Newton's Method used for? Assuming f(x) has a root, list three circumstances where Newton's Method will fail. Explain the meaning of the indefinite integral f(x) dx. How does an indefinite integral f(x) dx differ from a definite integral b and a f(x) dx ? What do each of these integrals represent? In your own words, explain the difference between the Fundamental Theorem of Calculus Part 1 and the Fundamental Theorem of Calculus part 2.

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