How do you find the limit of #x/sin(x)# as x approaches 0?
Manipulate the fundamental trigonometric limit to get
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To find the limit of x/sin(x) as x approaches 0, we can use the concept of L'Hôpital's Rule. By applying this rule, we differentiate both the numerator and denominator with respect to x. The derivative of x with respect to x is 1, and the derivative of sin(x) with respect to x is cos(x).
Therefore, the limit of x/sin(x) as x approaches 0 is equal to the limit of 1/cos(x) as x approaches 0.
Now, substituting x = 0 into the expression 1/cos(x), we get 1/cos(0) = 1/1 = 1.
Hence, the limit of x/sin(x) as x approaches 0 is equal to 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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