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

and the limit of the product is the product of the limits

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To find the limit of ((sin^2)3x) / (x^2) as x approaches 0, we can use the limit properties and trigonometric identities. By applying the limit properties, we can rewrite the expression as (sin^2(3x)) / (x^2) = (sin(3x))^2 / (x^2).

Next, we can use the trigonometric identity lim(x→0) sin(x) / x = 1. By substituting 3x for x, we have lim(x→0) sin(3x) / (3x) = 1.

Using this identity, we can rewrite the expression as lim(x→0) (sin(3x))^2 / (x^2) = (lim(x→0) sin(3x) / (3x))^2 = 1^2 = 1.

Therefore, the limit of ((sin^2)3x) / (x^2) 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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