Maclaurin Series
Not what you're looking for?
Given
The Maclaurin series for the inverse hyperbolic tangent is of the form x+x^3/3+x^5/5...x^7/7. Show that this is true through the third derivative term.
Purchase this Solution
Solution Summary
A relation involving a Maclaurin series is proven. Hyperbolic tangents are analyzed. The solution is detailed and well presented.
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
BrainMass Posting Solution
_____________________________________________________________
Posting # MATH 8689
Solution:
The problem asks us to find the Maclaurin series expansion of the function
f(x) = tanh-1x
Now, in general the Maclaurin series for any function is:
where f'(x) , f"(x), f(3)(x) ... f (n)(x) represent the first, second , third and nth derivatives of f(x) resp. and the Maclaurin series is expanded around the origin i.e. the derivatives are evaluated at x=0. We will simply use the above formula to deduce the answer.
Now let us look at the function f (x) = tanh-1x more closely and evaluate each of the above terms. The problem just asks us to go till the 3rd derivative so we shall stop at f(3)(x).
(i) 1st term of the formula is: f(0) . This means simply that ...
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts