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Example Question #1 : Maclaurin Series For Exponential And Trigonometric Functions
Write out the first three terms of the Taylor series about for the following function:
The Taylor series about x=a for a function is given by
For the first three terms (n=0, 1, 2) we must find the zeroth, first, and second derivative of the function. The zeroth derivative is just the function itself.
The derivatives were found using the following rules:
Now, using the above formula, write out the first three terms:
which simplified becomes
Example Question #2 : Maclaurin Series For Exponential And Trigonometric Functions
Find the Maclaurin Series of the function
up to the fifth degree.
The formula for an i-th degree Maclaurin Polynomial is
For the fifth degree polynomial, we must evaluate the function up to its fifth derivative.
The summation becomes
And substituting for the values of the function and the first five derivative values, we get the Maclaurin Polynomial