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

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To find the limit of (x + sin 2x)/(3x) as x approaches 0, we can use the limit properties and algebraic manipulation. First, we can rewrite sin 2x as 2sin x cos x. Then, we can divide both the numerator and denominator by x to simplify the expression. This gives us (1 + 2sin x cos x)/3. As x approaches 0, sin x approaches 0 and cos x approaches 1. Plugging these values into the expression, we get (1 + 2(0)(1))/3, which simplifies to 1/3. Therefore, the limit of (x + sin 2x)/(3x) as x approaches 0 is 1/3.

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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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