# How do you evaluate the limit #sin^3(2x)/sin^2(3x)# as x approaches #0#?

After the textbook result

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To evaluate the limit of sin^3(2x)/sin^2(3x) as x approaches 0, we can use the properties of limits and trigonometric identities. By applying the limit properties, we can simplify the expression:

lim(x→0) sin^3(2x)/sin^2(3x) = (lim(x→0) sin(2x))^3 / (lim(x→0) sin(3x))^2

Using the trigonometric identity lim(x→0) sin(x)/x = 1, we can rewrite the expression further:

= (2/2)^3 / (3/3)^2 = 1/1 = 1

Therefore, the limit of sin^3(2x)/sin^2(3x) as x approaches 0 is equal to 1.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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