Approximating functions with Taylor polynomials and error bounds

Intros

Lessons

Approximating Functions with Taylor Polynomials and Error Bounds
i) Taylor Polynomials and the Error Term

Examples

Lessons

Approximate ln 2 using the 3'rd degree Taylor Polynomial. Find the error term.
Find the 4th degree Taylor Polynomial centred around $a=0$ of $f(x)=e^x$ . Then approximate $e^2$ .
Find the 2nd degree Taylor Polynomial centred around $a=1$ of $f(x)=\sqrt{(x+1)}$ and the error term where $x \in [0,2]$ .
Show that $f(x)=e^x$ can be represented as a Taylor series at $a=0$ .
Show that $f(x)= \cos ?x$ can be represented as a Taylor series at $a=0$ .

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