Final answer:
The limit of sin6x/sin5x as x approaches 0 is found by using the sine limit property and simplifies to 6/5.
Step-by-step explanation:
To find the limit of sin6x/sin5x as x approaches 0, we can use the property that lim sin(kx)/kx as x approaches 0 is equal to 1 for any constant k.
For this question, we apply this property to both the numerator and the denominator separately.
We rewrite sin6x as 6*(sin6x/6x) and sin5x as 5*(sin5x/5x).
As x approaches 0, both (sin6x/6x) and (sin5x/5x) approach 1. Hence, the original limit simplifies to:
Lim x→0 sin6x/sin5x = Lim x→0 (6* sin6x/6x) / (5* sin5x/5x)
= 6/5
The answer to the limit is 6/5.