The Taylor series expansion for a* is: Σ (In a)" d = n! n =0 Write a MATLAB program that determines a* using the Taylor series expansion. The program asks the user to type a value for x. Use a loop for adding the terms of the Taylor series. If c, is the nth term in the series, then the sum S, of the n terms is S, = S,-1 + C - In each pass calculate the esti- mated error E given by E = Sn=1. . Stop adding terms when E<0.000001. Sn-1 The program displays the value of a*. Use the program to calculate: (a) 235 Compare the values with those obtained by using a calculator. (b) 6.31.7
Types of Loop
Loops are the elements of programming in which a part of code is repeated a particular number of times. Loop executes the series of statements many times till the conditional statement becomes false.
Loops
Any task which is repeated more than one time is called a loop. Basically, loops can be divided into three types as while, do-while and for loop. There are so many programming languages like C, C++, JAVA, PYTHON, and many more where looping statements can be used for repetitive execution.
While Loop
Loop is a feature in the programming language. It helps us to execute a set of instructions regularly. The block of code executes until some conditions provided within that Loop are true.
![The Taylor series expansion for \( a^x \) is:
\[
a^x = \sum_{n=0}^{\infty} \frac{(\ln a)^n}{n!} x^n
\]
Write a MATLAB program that determines \( a^x \) using the Taylor series expansion. The program asks the user to type a value for \( x \). Use a loop for adding the terms of the Taylor series. If \( c_n \) is the \( n \)th term in the series, then the sum \( S_n \) of the \( n \) terms is \( S_n = S_{n-1} + c_n \). In each pass calculate the estimated error \( E \) given by
\[
E = \left| \frac{S_n - S_{n-1}}{S_{n-1}} \right|
\]
Stop adding terms when \( E < 0.000001 \).
The program displays the value of \( a^x \). Use the program to calculate:
(a) \( 2^{3.5} \)
(b) \( 6^{3.17} \)
Compare the values with those obtained by using a calculator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3987b5-d473-4459-9b6d-f1c57ff7aeed%2F3f345147-168a-4ae7-a279-a3a290b7eb24%2Fk3hebhn_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Database System Concepts](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
![Starting Out with Python (4th Edition)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
![Database System Concepts](https://www.bartleby.com/isbn_cover_images/9780078022159/9780078022159_smallCoverImage.jpg)
![Starting Out with Python (4th Edition)](https://www.bartleby.com/isbn_cover_images/9780134444321/9780134444321_smallCoverImage.gif)
![Digital Fundamentals (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780132737968/9780132737968_smallCoverImage.gif)
![C How to Program (8th Edition)](https://www.bartleby.com/isbn_cover_images/9780133976892/9780133976892_smallCoverImage.gif)
![Database Systems: Design, Implementation, & Manag…](https://www.bartleby.com/isbn_cover_images/9781337627900/9781337627900_smallCoverImage.gif)
![Programmable Logic Controllers](https://www.bartleby.com/isbn_cover_images/9780073373843/9780073373843_smallCoverImage.gif)