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

One thing you should know going into this is that

This is an important identity in limit problems.

Limits can be multiplied, as follows:

graph{sinx/(2x^2-x) [-5.206, 5.89, -2.9, 2.65]}

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To find the limit of sinx/(2x^2-x) as x approaches 0, we can use algebraic manipulation and the properties of limits. First, we can factor out an x from the denominator to get sinx/x(2x-1). Then, we can simplify sinx/x to 1, as sinx/x approaches 1 as x approaches 0. Now, we are left with the limit of (1)/(2x-1) as x approaches 0. Plugging in 0 for x gives us 1/(2(0)-1) = 1/(-1) = -1. Therefore, the limit of sinx/(2x^2-x) as x approaches 0 is -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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