Final answer:
The limit of the function sin(2x) cos(3x) sin(5x) as x approaches 0 is 0, due to the properties of sine and cosine functions near 0.
Step-by-step explanation:
To calculate the limit of the function sin(2x) cos(3x) sin(5x) as x approaches 0, we can utilize the fact that sin(x) / x approaches 1 as x approaches 0. This is a well-known limit in calculus that can be applied when x is in radians.
As x approaches 0, each sine function behaves like its argument, meaning sin(2x) is approximately 2x, cos(3x) is approximately 1 (since cosine of 0 is 1), and sin(5x) is approximately 5x. Therefore, the product of these approximations is (2x) × 1 × (5x) which simplifies to 10x².
When calculating the limit of 10x² as x approaches 0, the result will be 0, since any real number, including 10, multiplied by 0² equals 0. Hence, the correct answer to the question is a) 0.