Task 1
Find the approximation value of Arcsin (0.5) by using TA around x = 0. Estimates the error joint in the calculation of arcsin (0.5) by using Rs. Enter an interval that certainly contains Arcsin (0.5).

Task 2
A periodic function f (x) is defined by
f(r)=f 7=22 f(- +0= /(.),
a) Sketch the graph of f (a) through 3 periods and calculate the Fourier array of f (x). Write the array on the form without expression like (,)”. b) b) What converge the Fourier row against when X = 3? Use x = 3 in the Fourier array of f (x) to find an exact value for the sum of the row
te’1 (2n — 1)2′

Task 3 Given the function by g(x)=x(1— x) for 0 < < 2.
Let H (x) be the even half-periodic expansion of G (X).

a) Write down the formula for H Wand sketch the graph of h (x) at the interval o E 1-6,61. Show that the Fourier row of this becomes
Fh(2) = 13 4 3(-14″* I coo (7).

c) Use the Fourier series to H (x) in x = 0 and x = 2 to find an exact value for the sum of the rows 1.2 E3 Hint: By evaluating FH (x) I x = 0 and x = 2, you get 2 equations with 2 unknown: r r V”‘ and £7.1-,(-07^’ as you can solve as a regular linear system.
Problem 4
Given the function by i(2) = – 1 for 0 < < 2.
to k (x) be the odd half-periodic expansion of 1 (x). Write down the formula for k (x) and sketch the graph of k (x) through 3 periods. How many paragraphs do we have to take from the Fourier series to 1( (X) to get an average square deviation le. than 10-?