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

*Task 2*

A periodic function f (x) is defined by

a) **Sketch the graph of f (x) 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

*Task 3*

Given the function by

Let H (x) be the even half–periodic expansion of G (X).

a) Write down the formula for H (x) and sketch the graph of h (x) at the interval . Show that the Fourier row of this becomes

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

Problem 4

Given the function by

La k (x) be the odd half–periodic expansion of J (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 K (X) to get an average square deviation less than.

*Task 1*

Determine the Laplace transform of the functions:

e) Rewrite the function using the Heaviside’s function and determine the Laplace transform of the function:

*Task 2*

Determine the inverse Laplace transform of the functions:

When using s–shift, determine the inverse Laplace transform of the functions:

*Task 3*

a) Determine the convolution of the function using the Laplace transformation. You will need the result from problem 2b)

b) Solve for x (t) using the Laplace transform.

Task 4

Use the Laplace transform to solve the differential equation with the initial values