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1.) Approximate e^x as 1+x and sin(x) as x-(x^3)/3 (maclaurin sin series). solve

ID: 2848703 • Letter: 1

Question

1.) Approximate e^x as 1+x and sin(x) as x-(x^3)/3 (maclaurin sin series). solve the resulting simplifies form of the above equation for x.


2.) Use newton-Raphson to perform 3 iterations to solve the full equation given above for x. Base you starting value on your answer to a. compute the approximate value relative errors for each iteration.


3.) a. for the full equation above show, by a simple test, that a root exists between x=0.01 and x=1

b. Use this information to perform 3 iterations beyond the starting values for x using secant rule. compute the approximate relative errors for each iteration.



Explanation / Answer

The following code implements the Newton-Raphson method for your problem:

You can plot the function with, for example: