# How do you find the limit of #(x / cos (-3x))# as x approaches #-oo#?

The limit does not exist

This can be verified with the graph of the function: graph{x/cos(0-3x) [-80, 80, -40, 40]}

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To find the limit of (x / cos (-3x)) as x approaches negative infinity, we can use the fact that the cosine function is bounded between -1 and 1. As x approaches negative infinity, the cosine of -3x will oscillate between -1 and 1. Since the numerator, x, is unbounded and the denominator, cos (-3x), is bounded, the limit of (x / cos (-3x)) as x approaches negative infinity does not exist.

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To find the limit of ( \frac{x}{\cos(-3x)} ) as ( x ) approaches negative infinity, we need to consider the behavior of the function as ( x ) becomes increasingly negative. Since cosine is a periodic function with a range of ([-1, 1]), the denominator ( \cos(-3x) ) oscillates between -1 and 1 as ( x ) approaches negative infinity. The numerator ( x ) is a linear function, which grows without bound as ( x ) becomes increasingly negative. As a result, the limit of the function ( \frac{x}{\cos(-3x)} ) as ( x ) approaches negative infinity does not exist.

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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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