# How do you find the limit of # (acota)/(sina) # as a approaches 0?

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Non-existing,

But, either way, both (a /sina) and cos a to 1.

So, the limit of the product = product of the limits

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To find the limit of (acot(a))/(sin(a)) as a approaches 0, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate the numerator and denominator separately and then take the limit as a approaches 0.

Differentiating the numerator, we get -acsc^2(a), and differentiating the denominator, we get cos(a).

Taking the limit as a approaches 0, we have (-acsc^2(a))/(cos(a)).

Substituting a = 0 into the expression, we get (-0csc^2(0))/(cos(0)).

Since csc(0) is undefined, we cannot directly substitute a = 0. However, we can simplify the expression further.

Using the trigonometric identity csc^2(a) = 1 + cot^2(a), we can rewrite the expression as (-a(1 + cot^2(a)))/(cos(a)).

Taking the limit as a approaches 0, we have (-0(1 + cot^2(0)))/(cos(0)).

Simplifying this expression, we get (0)/(1), which equals 0.

Therefore, the limit of (acot(a))/(sin(a)) as a approaches 0 is 0.

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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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