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 . 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

Engineer math assignment 5 and 6

Task 1
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) 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

Hint: By evaluating FH (x) I x = 0 and x = 2, you get 2 equations with 2 unknown: and As you can solve as a regular linear system.

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

Note: Every time you use the Laplace transform and get a function in the s-domain, remember to write for which s that function is valid.

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: