Find lim (x→0) [sin(x)cos(x) / (x + sin(2x))].
Choose 1 answer:
A) 2
B) 1
C) 1/3
D) The limit doesn't exist.

Question

Find lim (x→0) [sin(x)cos(x) / (x + sin(2x))]. Choose 1 answer: A) 2 B) 1 C) 1/3 D) The limit doesn't exist.

SnapAndSolve AI · Accepted Answer

To solve this limit, we can use the small angle approximations for sine and cosine functions: sin(x) ≈ x and cos(x) ≈ 1 when x is near 0.

The expression becomes:

lim (x→0) [sin(x)cos(x) / (x + sin(2x))] ≈ lim (x→0) [x * 1 / (x + 2x)] = lim (x→0) [x / 3x] = lim (x→0) [1/3] = 1/3.

Thus, the answer is C) 1/3.

Answer