How do you find the limit of #arcsin(x)/ arctan(x)# as x approaches 0?
We evaluate the limit first
We apply L'Hospitals Rule
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To find the limit of arcsin(x)/arctan(x) as x approaches 0, we can use L'Hôpital's rule. Taking the derivative of both the numerator and denominator, we get (1/sqrt(1-x^2))/(1/(1+x^2)). Simplifying this expression, we have (1+x^2)/sqrt(1-x^2). As x approaches 0, the numerator approaches 1 and the denominator approaches 1, so the limit 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.
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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