Question

# Tutorial#1: Applied Numerical Analysis using Excel software

Q1. Repeat Example 1.2. Compute the velocity at

t=8 s, with a step size of

(a) 1 and

(b) 0.5 s.

Can you make any statement regarding the errors of the calculation based on the results?

Q2. Determine the number of terms necessary to approximate cos(x) to 8 significant figures using

the Maclaurin series approximation

$cosx=1−x2/2+x4/4!−x6/6!+x8/8!−....$

Calculate the approximation using a value of x =0.3π. Find Absolute-True error, Relative True error,

Approximate-Relative error

Q3. The following infinite series can be used to approximate ex

$ex=1+x+x2/2+x3/3!+......+xn/n!$

:

a) Prove that this Maclaurin series expansion is a special case of the Taylor series

expansion with xi=0 and h=x.

b) Use the Taylor series to estimate f(x) = e

-x at xi+1=1 for xi=0.25. Employ the

zero-, first-, second-, and third-order versions and compute the true percent relative

error for each case

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