Use a known Taylor series to conjecture the value of .

Question

Use a known Taylor series to conjecture the value of  .

Quizplus · Accepted Answer

One known Taylor series that involves the constant e is the series for the exponential function:

e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + ...

If we substitute x = 0.0782 in this series, we get:

e^0.0782 = 1 + 0.0782 + (0.0782)^2/2! + (0.0782)^3/3! + (0.0782)^4/4! + ...

This can be approximated to the value:
1 + 0.0782 + 0.003038 + 0.000066676 + 0.000000938226 = 1.081084226

Multiplying this by 11 gives:
11 * 1.081084226 = 11eaa88b_9100_0782_a696_138a47cb355b_TB5869_11

Therefore, the best choice is C.

Use a Known Taylor Series to Conjecture the Value of