Find the third degreeTaylor polynomial centered at 1 for the function f(x)=x+3/x

Question

anonymous · Answer

Recall the formula for the Taylor Series/Maclaurin Series for $f(x)$ centered at $x=c$.  Here, $f^{(n)}(x)$ denotes the $n$th derivative of $f$.  Keep in mind that this equality is only valid within the radius of convergence of the series.  Also, note that $0!=1$.$$f(x)=\sum_{n=0}^\infty \frac{f^{(n)(c)}}{n!}(x-c)^n$$The third degree series is the one containing powers of $x$ up to 3.  Thus, plug and chug the following for $f(x)=\frac{x+3}{x}$.  Holler if you need more help!$$f(x) \approx f(c)+f'(x)(x-c)+\frac{f''(c)}{2}(x-c)^2+\frac{f'''(c)}{6}(x-c)^3$$Keep in mind that this polynomial is only an approximation as it contains 4 terms instead of an infinite number of terms.

anonymous · Answer

so what value do I put in for c