alingy1 said:Homework Statement
So, we are supposed to find the tenth taylor polynomial of sinx. On wolfram, I get a final term with x^11 at the end. How does that make sense?! According to the formula, n=10 so the maximum degree should be 10...
Homework Equations
Taylor polynomial formula.
The Attempt at a Solution
I would stick with what the formula tells me, but my homework wants me to write x^11. I DEMAND TO KNOW WHY AS ANY MATHEMATICIAN/SCIENTIST :) I am in grade 11.
The Tenth Taylor Polynomial for sinx is given by the formula:
P10(x) = x - x3/3! + x5/5! - x7/7! + x9/9!
The Tenth Taylor Polynomial for sinx is derived using the Taylor series expansion of sinx centered at x = 0. This involves finding the derivatives of sinx at x = 0 and substituting them into the general formula for the Taylor series.
The Tenth Taylor Polynomial for sinx provides a good approximation of the value of sinx for values of x close to 0. It can also be used to estimate the value of sinx for larger values of x by adding or subtracting the appropriate terms in the polynomial.
The Tenth Taylor Polynomial for sinx is an approximation of the value of sinx and therefore, it is not exact. The accuracy depends on the value of x and the number of terms used in the polynomial. As the number of terms increases, the accuracy also increases.
Yes, the Taylor series expansion can be used to find the Taylor Polynomial for any differentiable function, including other trigonometric functions such as cosx and tanx. The process is similar to finding the Tenth Taylor Polynomial for sinx.