Provide an appropriate response.
-For which of the following is the corresponding Taylor series a finite polynomial of degree 3?
A) $e ^ { - 2 x ^ { 3 } }$
B) $3 \ln ( x )$
C) $x ^ { 2 } \sin x$
D) $5 x ^ { 3 } + 2 x ^ { 2 } - 12$

Question

Provide an appropriate response.
-For which of the following is the corresponding Taylor series a finite polynomial of degree 3? 
A) $e ^ { - 2 x ^ { 3 } }$
B) $3 \ln ( x )$
C) $x ^ { 2 } \sin x$
D) $5 x ^ { 3 } + 2 x ^ { 2 } - 12$

Quizplus · Accepted Answer

The Taylor series of a polynomial of degree n is just the polynomial itself. Thus, option D, which is a polynomial of degree 3, has a Taylor series that is a finite polynomial of degree 3. The other options either have no Taylor series (option A), or have Taylor series that are infinite series (options B and C).

Provide an Appropriate Response e−2x3e ^ { - 2 x ^ { 3 } }e−2x3

Provide an Appropriate Response $e ^ { - 2 x ^ { 3 } }$