Discussion
\(\lim_{x \to 2} \frac{sinxcos2 - cosxsin2}{x - 2} =\)
Answer: B
The limit is 1.
The numerator is the expansion of a sine of a difference.
\[ \sin x\cos 2 - \cos x\sin 2 = \sin(x - 2) \]
So the expression is \(\frac{\sin(x - 2)}{x - 2}\), and with t = x - 2 tending to 0 it tends to \(\frac{\sin t}{t} \to 1\). The value 0 is what direct substitution gives in the numerator alone, and 2 or 4 bring the point x = 2 into the answer.
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