<p>I really dont get these questions I really appreciate clear help.</p>
<ol>
<li>The Taylor polynomial degree of 100 for the function f about x - 3 is given by
P(x) = (x-3)^2 -(x-3)^4 /2! + (x-3)^6 / 3! +....+ (-1)n+1 (x-3)^2n / n! + .... -(x-3)^100 / 50!</li>
</ol>
<p>What is the value of f^(30)(3)</p>
<p>answer is 30!/15! no idea why!</p>
<ol>
<li><p>The function f has derivatives of all orders for all real numbers, and f^(4)(x) = e^sin(x). If the third degree polynomial for f about x = 0 is used to approximate f on the interval [0,1], what is the Lagrange error bound for the maximum error on the interval [0,1]</p></li>
<li><p>The nth derivative of a function f at x = 0 is given by f^(n)(0) = (-1)^(n) (n+1)/(n+2)2^n. For all n > or equal to 0. What is P(3) of x?</p></li>
</ol>
<p>Any of these owuld help thanks!!!</p>