# Given #(sin(-2x)) / x# how do you find the limit as x approaches 0?

-2

one way

let u = -2x

OR

the term in green is indeterminate but as stated it is also a well known limit

you cannot use LHopital to prove this limit.

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To find the limit as x approaches 0 for the expression (sin(-2x)) / x, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate the numerator and denominator separately and then evaluate the limit of the resulting expression.

Differentiating the numerator, we get -2cos(-2x), and differentiating the denominator gives us 1.

Now, we can evaluate the limit of (-2cos(-2x)) / 1 as x approaches 0.

Substituting x = 0 into the expression, we have (-2cos(0)) / 1, which simplifies to -2.

Therefore, the limit as x approaches 0 for (sin(-2x)) / x is -2.

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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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