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WZ
Numerade Educator

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Problem 9 Medium Difficulty

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

$ \displaystyle \int_2^\infty e^{-5p}\ dp $

Answer

Convergent $\frac{1}{5} e^{-10}$

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Video Transcript

the problem is determine whether this Indian girl is convergent or there weren't. This is ai improper, Integral. So by definition, this is equal to the limit. He goes to infinity and integral of you two make your file D Then he from two. Two here. Then we need to find its anti derogative of the function e two next to foul his power. Basically no Teo, ruminative of negative one over negative five hams e to make you found his power. Do you really think this function is equal to make you one or five comes it. Thank you, Father. Hey, terms nine to five the Here we use chain rule. This is the car too. He to get your file. Yeah. His anti derivative of Eton mantel File piece power is equal to one overnight to five terms. Eat two negative five. She's power then this anti girl and Rico too. Lim. He goes to infinity of next negative one over a five terms e to make you foul. See from Teo. Ooh, See? Then we need to plant it plugging key. And to hear this is a conscious limit. He goes to infinity. Nick, you won over a five terms e to make you five. He minus into negative five times two is inactive and scholar, so things won t goes to infinity e to nectar of five teas. Power goes to Vero. His answer. If he caught too negative one over a five ham's negative e to neck, too. Hence power. So this is one over five Ham's. He too negative has power. This integral is converted. Ondas awhile is one over a file hams e to make you tense power.