Questions from Calculus


Q: (a) Find the second Taylor polynomial of √x at

(a) Find the second Taylor polynomial of √x at x = 9. (b) Use part (a) to estimate √8.7 to six decimal places. (c) Use the Newton–Raphson algorithm with n = 2 and x0 = 3 to approximate the solution of...

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Q: (a) Use the third Taylor polynomial of ln(1

(a) Use the third Taylor polynomial of ln(1 - x) at x = 0 to approximate ln 1.3 to four decimal places. (b) Find an approximate solution of the equation ex = 1.3 using the Newton–Raphson algorithm wit...

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Q: Use the Newton–Raphson algorithm with n = 2 to approximate

Use the Newton–Raphson algorithm with n = 2 to approximate the zero of x2 - 3x - 2 near x0 = 4.

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Q: Use the Newton–Raphson algorithm with n = 3 to approximate

Use the Newton–Raphson algorithm with n = 3 to approximate the solution of the equation e2x = 1 + e-x.

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Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 1 – ¾ + 9/16 – 27/64 + 81/256 - …

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Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 52/6 + 53/62 + 54/63 + 55/64 + 56/65 + …

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Q: If f (x) = 2 - 6 (x -

If f (x) = 2 - 6 (x - 1) + 3/2! (x - 1)2 – 5/3! (x - 1)3 + 1/4! (x - 1)4, what are f ’’(1) and f ’’’(1)?

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Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 1/8 + 1/82 + 1/83 + 1/84 + 1/85 + …

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Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 22/7 - 25/72 + 28/73 - 211/74 + 214/75 - …

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Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 1/(m + 1) + m/(m + 1)2 + m2/(m + 1)3 + m3/(m + 1)4 +…, where m is a positive number

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