Answer: 1.
- A 0
- B 1
- C π
- D undefined
Correct answer: B. 1
Explanation: Since (sinx)/x → 1 as x → 0, we need k = 1.
f(x)=|x| is perfectly continuous at x=0 (no break, no jump), but the curve has a sharp corner there: approaching from the left gives slope -1 and from the right gives slope +1 - since these one-sided derivatives disagree, the function is not differentiable at that point.
Concept context
When a function has no breaks (continuity) and when it has a well-defined slope (differentiability), plus rules for differentiating implicit, inverse trig, exponential, log, and parametric functions.