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## Homework Statement

Evaluate the lim as x approaches 3 of (x/x-3) times the integral from 3 to x of (sint/t)dt

- Thread starter Jbjohnson15
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- #1

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Evaluate the lim as x approaches 3 of (x/x-3) times the integral from 3 to x of (sint/t)dt

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So, what did you already do to solve the problem?

How do you usually solve "0/0" situations?

How do you usually solve "0/0" situations?

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[f(x+h)-f(x)]/h ? I'm really not sure. What would be the h? 3? I'm so lost.

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How would you resolve a "0/0"-situation with the aid of derivatives????

L'hopital rule

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[tex]\lim_{x\rightarrow 3}{\frac{x\int_3^x{\frac{\sin(t)}{t}dt}}{x-3}}[/tex]

Try applying l'Hopitals rule on that. You are correct that the integral will not disappear, but the limit will become simpler...

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For ease, define

[tex]F(x)=\int_3^x{\frac{\sin(t)}{t}dt}[/tex]

What is [tex]F^\prime(x)[/tex] (this is basically the fundamental theorem of calculus).

Now you want to calculate the derivative of xF(x). How would you do this? (hint: product rule)

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- #12

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Yes, that is correct. Now take the limit of that expression. What do you get?

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Yes, sin(3) seems to be the correct answer.

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