Determine if the given function can be extended to a continuous function at x = 0. If so, approximate the extended
function's value at x = 0 (rounded to four decimal places if necessary). If not, determine whether the function can be
continuously extended from the left or from the right and provide the values of the extended functions at x = 0.
Otherwise write "no continuous extension."
-$$f ( x ) = ( 1 + 2 x ) ^ { 1 / x }$$
A) f(0) = 7.3891
B) No continuous extension
C) f(0) = 5.4366
D) f(0) = 2.7183

Question

Quizplus · Accepted Answer

The function $ f(x) = (1 + 2x)^{1/x} $ can be extended to a continuous function at $ x = 0 $ by evaluating the limit as $ x $ approaches 0. This limit is $ e^2 $, which is approximately 7.3891.

Determine If the Given Function Can Be Extended to a Continuous