MXB103

Question 1
Express the binary number 1010101.0101 in decimal format.
Assign the answer to x:

Question 2
Complete the code and plot the function

on the interval .

Question 3
Calculate the absolute and relative errors when approximating by the fraction

Question 4
The Taylor polynomial of degree centred on for the function is given by:

Complete the code that approximates by evaluating at .
The code should use element-wise operations, must use MATLAB's sum function, and must not use a for loop.

Question 5
Let be the Taylor polynomial of degree (at most) centred on for the function .
Complete the function taylor_cos that takes and as inputs and returns evaluated at .
Your function must use a for loop and should not use any anonymous functions.
Hint: Find first.

Question 6
Complete the function approx_root2 that takes as an input and calculates the following approximation to :

Your code must use a for loop to compute the sum.

Question 7
Complete the below function swap_elements that takes two arrays/vectors as inputs and interchanges their second and fith elements.

Question 8
Complete the function array_product to compute the product of the elements of an array v.
Your code must use a for loop and must not use MATLAB's prod function.

Question 9
Recreational and elite runners targeting a certain race distance are often interested in the average pace they are required to run to reach a certain time goal.
Complete the function required_pace (expressed in hours, minutes and seconds per kilometre) required to finish precisely in the goal time.
Your code must use MATLAB's floor function.

Question 10
Complete the function turning_points that solves for a given polynomial .
Your code must use MATLAB's roots function.