Determine If the Given Function Can Be Extended to a Continuous

question 137

Multiple Choice

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."
- $$f ( x ) = \frac { \tan x } { x }$$

• A) f(0) = 1 only from the right
• B) No continuous extension
• C) f(0) = 1
• D) f(0) = 1 only from the left

---

Definitions:

Type I Error

Incorrectly refuting a correct null hypothesis, also labeled as a "false positive."

Null Hypothesis

A hypothesis stating there is no significant difference or effect, used as a starting point for statistical testing.

Significance Level

A threshold for determining whether an observed effect is statistically significant, often set at 0.05.

Alternative Hypothesis

A hypothesis that contradicts the null hypothesis, proposing a new effect or relationship.