# How do you find the limit of #(sin2x)/x# as x approaches infinity?

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To find the limit of (sin2x)/x as x approaches infinity, we can use the limit properties and trigonometric identities. By applying the limit definition, we have:

lim(x→∞) (sin2x)/x = lim(x→∞) sin(2x)/x

Using the Squeeze Theorem, we know that -1 ≤ sin(2x) ≤ 1 for all x. Therefore, we can write:

-1 ≤ sin(2x)/x ≤ 1/x

As x approaches infinity, the right side of the inequality, 1/x, approaches 0. Hence, we can conclude that:

lim(x→∞) (sin2x)/x = 0

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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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