A 4th order Taylor polynomial is written for a function with a range of y > 0 and all non-zero derivatives. Assuming the terms are listed in ascending order of degree, which term contains the third derivative of the function?

h(x) is a continuous function with continuous derivatives. Using the values given in the table what is the 2nd term of a Taylor polynomial centered at x = 2?

 $2\ +\sqrt{3}\left(x-3\right)\ +\ 10\left(x-3\right)^2\ +\pi\left(x\ -\ 3\right)^3$  is a Taylor polynomial for g(x) centered at 3.  Which term contains g"(3) as part of its coefficient ?

 $2\ +\sqrt{3}\left(x-3\right)\ +\ 10\left(x-3\right)^2\ +\pi\left(x\ -\ 3\right)^3$  is a Taylor polynomial for g(x) centered at 3.  Which equation is the correct set-up to find the value of g"(3)?

 $T_4\left(x\right)\ =\ 2\ -\ 2\left(x\ -\ a\right)\ +\sqrt{5}\left(x-a\right)^2-\frac{\pi}{2}\left(x-a\right)^3+\left(x-a\right)^4$  is a Taylor polynomial for a function, f(x), centered at a.  What is f(a)?

 $T_4\left(x\right)\ =\ 2\ -\ 2\left(x\ -\ a\right)\ +\sqrt{5}\left(x-a\right)^2-\frac{\pi}{2}\left(x-a\right)^3+\left(x-a\right)^4$  is a Taylor polynomial for a function, f(x) centered at a.  What is f '''(a) ?

given:  $f\left(0\right)\ =\ 0,\ f'\left(0\right)\ =\ 1,\ f"\left(0\right)\ =\ -1,\ f'''\left(0\right)\ =\ 2$ A polynomial using these values can be called both Taylor and MacLaurin .

given:  $f\left(0\right)\ =\ 0,\ f'\left(0\right)\ =\ 1,\ f"\left(0\right)\ =\ -1,\ f'''\left(0\right)\ =\ 2$ Which of these is the 3rd order Taylor polynomial for f(x), centered at x = 0.  

This is true:  $e^x=1+x+\frac{x^2}{2!}+\frac{x^{3^{ }}}{3!}+\frac{x^4}{4!}+...$  

Is this true, too?  $e^2=1\ +\ 2+\frac{2^2}{2!}+\frac{2^{3^{ }}}{3!}+\frac{2^4}{4!}...$