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Jbjohnson15
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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
The limit does not exist because as x approaches 3, the denominator (x-3) approaches 0, causing the expression to become undefined.
The limit does not exist because when the denominator of a rational function approaches 0, the function becomes undefined.
Yes, you can simplify the expression by factoring the numerator and simplifying the integral, which results in the expression (1/x)∫(sin t/t)dt. However, this does not change the fact that the limit does not exist.
No, L'Hopital's rule can only be applied to limits of the form 0/0 or ∞/∞. In this case, the limit is of the form 0/0, but the rule cannot be applied because it requires the expression to be a quotient of two functions, which is not the case here.
Yes, the expression is undefined when x=3, as the denominator becomes 0. Therefore, x cannot equal 3 for the expression to be defined.