How do you find the limit of # ( x + sin(x) ) / (x) # as x approaches 0?
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To find the limit of (x + sin(x))/x as x 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 again.
Differentiating the numerator, we get 1 + cos(x), and differentiating the denominator gives us 1.
Taking the limit as x approaches 0, we have (1 + cos(0))/1, which simplifies to (1 + 1)/1 = 2/1 = 2.
Therefore, the limit of (x + sin(x))/x as x approaches 0 is equal to 2.
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The limit of ( \frac{x + \sin(x)}{x} ) 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.
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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