Question

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval $\ln x = \frac{2}{\sqrt{x}}$, $(2, 4)$

          Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval
$\ln x = \frac{2}{\sqrt{x}}$, $(2, 4)$
        
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval
ln x = (2)/(√(x)), (2, 4)

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval lnx=(2)/(sqrt(x)), Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval 2 1nc= (2,4)
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Transcript

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0:00 All right.
00:01 The question asks you to use the intermediate value theorem to show that there is a root of that polynomial in the interval from 1 to 2.
00:10 Okay, so let's just look.
00:12 This is defined at the endpoints, even though it's not included in the interval.
00:16 So let's just look at what the value is.
00:20 We'll even call it, let's just call it f of x equals x the 4 minus x or plus x minus 3.
00:28 Let's make sure we copy things downright.
00:30 F of 1, since it is defined at 1, is 1 plus 1 minus 3, is negative 1.
00:37 And then f of 2 is 2 to 416 plus 2 minus 3 is positive 15.
00:46 So let's just look on a graph where that is...
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