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."
-$$f ( x ) = \frac { \cos 2 x } { | 2 x | }$$
A) f(0) = 2 only from the left
B) No continuous extension
C) f(0) = 2
D) f(0) = 2 only from the right

Question

Quizplus · Accepted Answer

The function $\frac{\cos 2x}{|2x|}$ cannot be continuously extended at $x = 0$ because the denominator becomes zero and the absolute value causes a discontinuity that cannot be resolved from either side.

Determine If the Given Function Can Be Extended to a Continuous