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# (a) Graph the functions $f(x) = \frac{1}{x^{1.1}}$ and $g(x) = \frac{1}{x^{0.9}}$ in the viewing rectangles $[0, 10]$ by $[0, 1]$ and $[0, 100]$ by $[0, 1]$.(b) Find the areas under the graphs of $f$ and $g$ from $x = 1$ to $x = t$ and evaluate for $t = 10, 100, 10^4 , 10^6 , 10^{10}$, and $10^{20}$.(c) Find the total area under each curve for $x \ge 1$, if it exists.

## a. b. 990c. $g(x)=\frac{1}{x^{0.9}}$ for $x \geq 1$ does not exist.

#### Topics

Integration Techniques

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

for this problem. I just gave you some ideas on how to do the party part. See Poppy into girl off from one to t the axe. But communications, this is Echo two integral from one t act to make you one one point one of the ice. On this he caught you. Make it ten ums. Nice to right. Zero on one from one tea. Anyone can write a thesis can times one minus to make you zero point. What, then? Just popping ten hundred and out. The numbers similarly integral off, Jax, this is equal to is equal to ten hams. Axe too. Their point one from one tea. This hand. I need to Varel point one minus one now sold Plumbing those numbers. This is a B or C. The total area and each turf for extra. It is on one. This thing, can't you what the function affects this is equal to the limit. He goes to financially of the integral of one to t of the function. That fact? Yes. And when he goes to infinity, he to make you their appoint. One goes to Vero. It's the limit is equal to ten. And for the function Do you wax? Then it He goes to infinity into girl. Want Teo or function? Deal works the ex. We can see when t goes to infinity. He to their upon one's power goes to infinity. This is Bauer.

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#### Topics

Integration Techniques

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp