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1) Why is the integral from x=1 to x=3 of f(x)=1/(x-2)^(2/3) improper?

2) Find the length of the arc of y=x^(3/2) between the points (1,1) and (4,8).

3) Find the limit of the sequence a sub n={sin(n)/n}, if it exists.

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02:05

Evaluating an Improper Integral In Exercises $9-12$ , explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converges.$$\int_{3}^{4} \frac{1}{(x-3)^{3 / 2}} d x$$

00:57

Explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converges.$$\int_{3}^{4} \frac{1}{\sqrt{x-3}} d x$$

01:50

Evaluating an Improper Integral In Exercises $9-12$ , explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converges.$$\int_{0}^{4} \frac{1}{\sqrt{x}} d x$$

Transcript

from the given question we need to know why is the integral front X is equal to one. two. X is equal to three. A five X is equivalent to one divided by X -2 whole power two liberated by three is improper. This is that portion. Now given fr if X is equal to one divided by X -2. Full Pavan. Two reverted bank three integral 123 one divided by X -2 Whole Papa. two reverted by three V. X. That integrated is not they find and X. Is it pronto? So this season improper integral. Yes but integral converges then. Weird. The value Now the integral 1-3 One divided by X -2 whole power to reverted by three. That is equal to we can write a desk Integral 1-3 B. X directed by X -2 whole power to reverted by three. Place integral 2-3 B. It’s diverted by x minus two. Full power to riveted by three. Since both integral converges that is equal. Do we can write it as leave me B. Two.…

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