Answer: The final result is 37³ * sin(72)
Explanation:
To evaluate the limit of the expression lim(x->72) [37³sin(x)], we can break down the problem into steps while noting the Limit Laws being utilized.
Step 1: Start with the expression: 37³sin(x)
No limit laws are applied at this point.
Step 2: Apply the constant multiple rule: lim(x->72) [37³sin(x)] = 37³ * lim(x->72) [sin(x)]
The constant multiple rule allows us to bring the constant term (37³) outside the limit.
Step 3: Apply the limit of sine function: lim(x->72) [sin(x)] = sin(72)
As x approaches 72, the sine function approaches sin(72).
Step 4: Combine the results: 37³ * lim(x->72) [sin(x)] = 37³ * sin(72)
Using the constant multiple rule, we combine the constant term (37³) with the result of the limit of the sine function.