How do you use L'hospital's rule to find the limit #lim_(x->oo)xsin(pi/x)# ?
To use L'Hôpital's Rule to find the limit lim(x→∞) x*sin(π/x), follow these steps:
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Identify the indeterminate form of the limit as x approaches infinity, which is 0*∞.
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Rewrite the limit as a fraction: lim(x→∞) sin(π/x) / (1/x).
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Take the derivatives of the numerator and denominator separately.
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Evaluate the derivatives and substitute them back into the original limit expression.
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Repeat steps 3 and 4 as needed until the limit is no longer in an indeterminate form.
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Evaluate the limit using the new expression.
Remember that L'Hôpital's Rule can only be applied when both the numerator and denominator approach either 0 or infinity as x approaches the limit.
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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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- How do you use the direct Comparison test on the infinite series #sum_(n=1)^ooarctan(n)/(n^1.2)# ?
- How do you use the ratio test to test the convergence of the series #∑k/(3+k^2) # from k=1 to infinity?

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