In(1 + x) can be approximated using the following Maclaurin series expansion: x2 In(1 + x) = %=1(–1)n-1 * = x - x2/2 + x3/3 - x4/4 for (12x>-1)
Use the pseudocode below to implement the expansion as a MATLAB function. Calculate the true percent relative error for each iteration. The loop should terminate when the true percent relative error of falls below 0.0001. The true value can be found using the MATLAB's log function and the approximation is found using the Taylor series expansion. The input to the function should be the value x. Test your code with x = 0.25.
FUNCTION my_In(x)
tpre = 100
approx = 0
true_value = In(1+x)
n = 1
DO
new_term = (–1)n-1 X
approx = approx + new_term
tore-[true value – approx * 100 tpre = true value
n= n +1
IF tpre < 0.0001 OR n > 1000
EXIT
ENDIF
END
DO
Display approx
Display tpre
END my_In
Hint 1 - Don't use 'EXIT' to break out of your loop in MATLAB (this will exit MATLAB).