Question

Lim sin(ax) × cos(bx) / sinc(x) tends to 0
A) 0
B) 1
C) -1
D) Undefined

Answer 1

Using properties of sine and cosine functions, the limit of sin(ax) × cos(bx) / sinc(x) as x tends to 0 is found to be 0.

Step-by-step explanation:

The limit of sin(ax) × cos(bx) / sinc(x) as x tends to 0 can be found using L'Hôpital's Rule and the fact that sin(0) = 0. However, because the sinc function is defined as sinc(x) = sin(x) / x for x ≠ 0 and sinc(0) = 1 (by the definition of the function), this limit is equivalent to evaluating sin(ax) × cos(bx) as x approaches 0. Since sin(0) = 0 and cos(0) = 1, the limit as x approaches 0 is simply 0 × 1, which is 0. Therefore, the correct answer is A) 0.