# What is the taylor series used for?

See the explanation below :-

Taylor series is used for the expansion of any continuously differentiable function in the term of a polynomial .

The formula for Taylor expansion is given below :-

For eg :

The Taylor series for

which is a polynomial of

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The Taylor series is used to represent functions as infinite series of polynomial terms, providing a way to approximate functions as polynomials near a given point. This is particularly useful in calculus and mathematical analysis for approximating functions, computing derivatives, and solving differential equations. It is also applied in various fields such as physics, engineering, and computer science for solving problems involving non-linear functions.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find taylor polynomials of degree n approximating #5/(2-2x)# for x near 0?
- How do you find the Maclaurin Series for #e^(sinx)#?
- How do you find the Taylor remainder term #R_3(x;0)# for #f(x)=1/(2+x)#?
- How do you find the smallest value of #n# for which the Taylor series approximates the function #f(x)=e^(2x)# at #c=2# on the interval #0<=x<=1# with an error less than #10^(-6)#?
- How to, using Taylor series approximation , estimate the value of π, when arctan(x) ≈ x-x3/3+x5/5-x7/7 ?

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