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WZ
Numerade Educator

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Problem 4 Medium Difficulty

(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.

Answer

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

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Video Transcript

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