# How do you find the limit of #sin(x^2−4)/(x−2) # as x approaches 2?

Write it in a form that allows us to use

Here is the graph.

graph{sin(x^2-4)/(x-2) [-4.305, 8.185, -1.205, 5.04]}

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To find the limit of sin(x^2−4)/(x−2) as x approaches 2, we can use the limit properties and algebraic manipulation. By substituting x=2 into the expression, we get an indeterminate form of 0/0. To resolve this, we can factor the numerator as (sin(x+2))(sin(x-2)) and cancel out the common factor of (x-2). After canceling, we are left with sin(x+2). Now, we can substitute x=2 into sin(x+2) to find the limit. By doing so, we get sin(4), which equals 0. Therefore, the limit of sin(x^2−4)/(x−2) as x approaches 2 is 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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