37. Prove that lim⁡(x→a) √x=√a if a≻0. [Hint: Use |√x-√a|=|x-a|/(√x-√a).]

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37. Prove that lim⁡(x→a) √x=√a if a≻0. [Hint: Use |√x-√a|=|x-a|/(√x-√a).]

Calculus: Early Transcendentals
Chapter 2: Limits and Derivatives
Section 2.4: The Precise Definition of a Limit
Problem 37

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37. Prove that 0:05:11

37. Prove that lim⁡(x→a) √x=√a if a≻0. [Hint: Use |√x-√a|=|x-a|/(√x-√a).]

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Автор

So there are two corrections, firstly, you replace the 1 by, say, (a/2) and then get an upper bound for the denominator. Then you get the delta value the same way you did. Now, you have to take the minimum of this delta value and (a/2), to ensure that all your inequalities will hold.

literallyjustayoutubecomme
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Hmm, the hint here is incorrect, the one in the thumbnail is correct. The proof is anyway incorrect, you assume implicitly that a\geq 1, which is not necessarily true. You can only assume that it is greater than some positive number, since it is positive, then work with that

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