Using Taylor Theorem to Estimate Error Using Approximation

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Taylors theorem tells us that:

En(x) ≤ $\frac {M}{(n+1)!}|x-a|^n$ $^+$ $^1$

Use this to estimate the error in using the approximation.

$sin(x) ≈ x$ - $\frac {x^3}{3!}$ on the interval [-1,1]

Assuming x and a are endpoints. Does endpoint mean the interval? So x and a are -1 and 1 respectively?

M is supposed to be the upper bound.

Also I am unsure of what n is supposed to be.

How do you choose a suitable n value? Also how do you find M?

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$$ E_4(x) \le \frac {M}{(4+1)!}|x-a|^5 = \frac {1}{120}(1)^5 = 1/120$$

Note that since the coefficient of $x^4$ is $0$, the error term is $E_4.$