# What is the limit of #(4x − sin4x)/(4x − tan4x)# as x approaches 0?

1

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I'll use l'Hospital's rule.

Here is the graph:

graph{(4x-sin(4x))/(4x-tan(4x) [-4.375, 3.42, -1.795, 2.1]}

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The limit of (4x − sin4x)/(4x − tan4x) 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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