Question

13-19. Finding roots with Newton's method For the given function f and initial approximation $x_0$, use Newton's method to approximate a root of f. Stop calculating approximations when two successive approximations agree to five digits to the right of the decimal point after rounding. Show your work by making a table similar to that in Example 1. 13. $f(x) = x^2 - 10; x_0 = 3$ 14. $f(x) = x^3 + x^2 + 1; x_0 = -1.5$ 15. $f(x) = \sin x + x - 1; x_0 = 0.5$ 16. $f(x) = e^x + x - 5; x_0 = 1.6$ 17. $f(x) = \tan x - 2x; x_0 = 1.2$ 18. $f(x) = x \ln (x + 1) - 1; x_0 = 1.7$ 19. $f(x) = \cos^{-1} x - x; x_0 = 0.75$

          13-19. Finding roots with Newton's method For the given function
f and initial approximation $x_0$, use Newton's method to approximate
a root of f. Stop calculating approximations when two successive
approximations agree to five digits to the right of the decimal point
after rounding. Show your work by making a table similar to that in
Example 1.
13. $f(x) = x^2 - 10; x_0 = 3$
14. $f(x) = x^3 + x^2 + 1; x_0 = -1.5$
15. $f(x) = \sin x + x - 1; x_0 = 0.5$
16. $f(x) = e^x + x - 5; x_0 = 1.6$
17. $f(x) = \tan x - 2x; x_0 = 1.2$
18. $f(x) = x \ln (x + 1) - 1; x_0 = 1.7$
19. $f(x) = \cos^{-1} x - x; x_0 = 0.75$

13-19. Finding roots with Newton's method For the given function
f and initial approximation x0, use Newton's method to approximate
a root of f. Stop calculating approximations when two successive
approximations agree to five digits to the right of the decimal point
after rounding. Show your work by making a table similar to that in
Example 1.
13. f(x) = x^2 - 10; x0 = 3
14. f(x) = x^3 + x^2 + 1; x0 = -1.5
15. f(x) = sin x + x - 1; x0 = 0.5
16. f(x) = e^x + x - 5; x0 = 1.6
17. f(x) = tan x - 2x; x0 = 1.2
18. f(x) = x ln (x + 1) - 1; x0 = 1.7
19. f(x) = cos^-1 x - x; x0 = 0.75

Added by Dustin G.

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