Numerical Analysis & it’s applications 1. (Floating-Point Arithmetic, Taylor Polynomials, Horner's Method;hyperbolic arcsine functionIt is known that the ninth Taylor polynomial T(x) of thef(x) = arcsinh(x) = In(x + V1+ x2)centered at zero is13T(x) = x -635+115240112In particular, one can approximate the values of the hyperbolic arcsine about zero by the corresponding values of this Taylor polynomial,In(x + V1+x²2) = T(x),provided that |x| is small enough. Based on this fact, realize the following plan of obtaining an approximation of In(25/19).(i) Show first thatx + V1+x2 = 25/19 + x = 132/475.Thus in view of (1.1) we can approximate In(25/19) by T(132/475):In(25/19) z T(132/475).

Name: Numerical Analysis & it’s applications 1. (Floating-Point Arithmetic,
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Description: Numerical Analysis & it’s applications 1. (Floating-Point Arithmetic, Taylor Polynomials, Horner's Method;hyperbolic arcsine functionIt is known that the ninth Taylor polynomial T(x) of thef(x) = arcsinh(x) = In(x + V1+ x2)centered at zero is13T(x) =

(i) We have to show that x+1+x2=2519⇔x=132475 Part 1) If part, If x+1+x2=2519 then x=132475…

Answered: (i) Show first that x + V1+ x2 = 25/19…

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(i) Show first that x + V1+ x2 = 25/19 + 1 = 132/475. %3D

Advanced Engineering Mathematics

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Chapter2: Second-order Linear Odes

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Numerical Analysis & it’s applications

1. (Floating-Point Arithmetic, Taylor Polynomials, Horner's Method;
hyperbolic arcsine function
It is known that the ninth Taylor polynomial T(x) of the
f(x) = arcsinh(x) = In(x + V1+ x2)
centered at zero is
1
3
T(x) = x -
6
35
+
1152
40
112
In particular, one can approximate the values of the hyperbolic arcsine about zero by the corresponding values of this Taylor polynomial,
In(x + V1+x²2) = T(x),
provided that |x| is small enough. Based on this fact, realize the following plan of obtaining an approximation of In(25/19).
(i) Show first that
x + V1+x2 = 25/19 + x = 132/475.
Thus in view of (1.1) we can approximate In(25/19) by T(132/475):
In(25/19) z T(132/475).

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