Calculate f (x) = x 10e

−x for the following values of x.

a. x = 1.

b. x = 10.

c. x = 100.

d. x = 1000.

Using your results, infer the value of limx→∞ x 10e

−x

. Can you guess the value of limx→∞ x n

e

−x

, for any n > 0? Check your guess by computing some values, or by using a computer package (such as Wolfram Alpha).