Question

The power series for the exponential function centered at 0 is $e^x = \sum_{k=0}^{\infty} \frac{x^k}{k!}$ for $-\infty < x < \infty$. Find the power series for the following function. Give the interval of convergence for the resulting series. $f(x) = 7x^6e^x$ Which of the following is the power series representation for $f(x)$? A. $7 \sum_{k=0}^{\infty} \frac{x^6e^{xk}}{k!}$ B. $7 \sum_{k=0}^{\infty} \frac{x^{k+6}}{k!}$ C. $7 \sum_{k=0}^{\infty} \frac{x^{6k}}{k!}$ D. $6 \sum_{k=0}^{\infty} \frac{x^{7k}}{k!}$ The interval of convergence is $ (Simplify your answer. Type your answer in interval notation.)

          The power series for the exponential function centered at 0 is $e^x = \sum_{k=0}^{\infty} \frac{x^k}{k!}$ for $-\infty < x < \infty$. Find the power series for the following function. Give the interval of convergence for the resulting series.
$f(x) = 7x^6e^x$
Which of the following is the power series representation for $f(x)$?
A. $7 \sum_{k=0}^{\infty} \frac{x^6e^{xk}}{k!}$
B. $7 \sum_{k=0}^{\infty} \frac{x^{k+6}}{k!}$
C. $7 \sum_{k=0}^{\infty} \frac{x^{6k}}{k!}$
D. $6 \sum_{k=0}^{\infty} \frac{x^{7k}}{k!}$
The interval of convergence is $
(Simplify your answer. Type your answer in interval notation.)

The power series for the exponential function centered at 0 is e^x = ∑k=0^∞(x^k)/(k!) for -∞ < x < ∞. Find the power series for the following function. Give the interval of convergence for the resulting series.
f(x) = 7x^6e^x
Which of the following is the power series representation for f(x)?
A. 7 ∑k=0^∞(x^6e^xk)/(k!)
B. 7 ∑k=0^∞(x^k+6)/(k!)
C. 7 ∑k=0^∞(x^6k)/(k!)
D. 6 ∑k=0^∞(x^7k)/(k!)
The interval of convergence is (Simplify your answer. Type your answer in interval notation.)

Added by Remedios J.

Question

Please give Ace some feedback