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- Thread starter maceng7
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SammyS

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You're right, there is no general rule.

Whatever gives better cancellation of offending factors is often a good choice.

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What's a good way to start then? Putting the function whose derivative is simpler on the bottom or top or does it even matter?

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SammyS

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It's not always that simple, (Pardon the joke.) although that does often work.

I have seen cases where the derivative of top or bottom gets more complicated than the original, but the result affords just the right amount of cancelling with the other derivative so that the overall result is nicely behaved.

--- no example off the top of my head.

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Alright I think I did this one correctly

lim x--> 1

I found this limit by putting ln(x) in the numerator and tan(∏x/2) in the denominator. I used l'hospital's rule once and found it to be 1/∞ so my answer is 0. Is this correct?

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SammyS

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Please show your steps.Alright I think I did this one correctly

lim x--> 1^{+}ln(x) * tan(∏x/2)

I found this limit by putting ln(x) in the numerator and tan(∏x/2) in the denominator. I used l'hospital's rule once and found it to be 1/∞ so my answer is 0. Is this correct?

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Dick

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Alright I think I did this one correctly

lim x--> 1^{+}ln(x) * tan(∏x/2)

I found this limit by putting ln(x) in the numerator and tan(∏x/2) in the denominator. I used l'hospital's rule once and found it to be 1/∞ so my answer is 0. Is this correct?

No, it's not right. How exactly did you do that? You don't just 'put something into the denominator'. a*b is not equal to a/b, it is equal to a/(1/b).

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It appears we are all giving the same advice. @maceng7 is what we are saying making any sense?

Let a = ln(x) and b = tan(pix/2). As dick mentioned, a*b is entirely different from a/b. By putting the b in the denominator, you've created a new function, entirely different from the original; and when you evaluate the limit of a/b, the result you get tells you nothing of the limit for a*b. This is true, because a*b and a/b are different functions.

Let a = ln(x) and b = tan(pix/2). As dick mentioned, a*b is entirely different from a/b. By putting the b in the denominator, you've created a new function, entirely different from the original; and when you evaluate the limit of a/b, the result you get tells you nothing of the limit for a*b. This is true, because a*b and a/b are different functions.

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Ray Vickson

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NO: if it is 0/∞ you are done: the answer = 0 and there is no need for l'Hospital's rule.

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SammyS

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But asNO: if it is 0/∞ you are done: the answer = 0 and there is no need for l'Hospital's rule.

Let's wait to hear back from OP .

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