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Problem 7.3: Rewrite an Indeterminate Expression of the form $1^\infty$ and Use \L'Hôpital's Rule Evaluate the following limit: $\lim_{x \to \infty} (1 - \frac{2}{x})^{5x}$

          Problem 7.3: Rewrite an Indeterminate Expression of the form $1^\infty$ and Use \L'Hôpital's Rule
Evaluate the following limit:
$\lim_{x \to \infty} (1 - \frac{2}{x})^{5x}$
        
Problem 7.3: Rewrite an Indeterminate Expression of the form 1^∞ and Use Ł'Hôpital's Rule
Evaluate the following limit:
limx →∞ (1 - (2)/(x))^5x

Added by Danny B.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Problem 7.3: Rewrite an Indeterminate Expression of the form 1^(infty ) and Use L'Hôpital's Rule Evaluate the following limit: lim_(x->infty )(1-(2)/(x))^(5x) Problem 7.3: Rewrite an Indeterminate Expression of the form 1 and Use L'Hopital's Rule Evaluate the following limit: lim
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Transcript

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00:01 So given this limit, let's just use the method of replacement.
00:03 Replace all the x values that i have with 7, see what limit i get.
00:10 So 7 squared minus 2 times 7 minus 25.
00:14 Okay.
00:15 This will end up being 49 minus 14.
00:21 And we know that 49 minus 14 is 35 minus 25 minus 25 will be positive 10.
00:29 Okay, all over 7 times 7 minus 7 squared.
00:36 7 squared minus 7 squared, this is going to be 0.
00:40 But note that, oh, excuse me, this is 35.
00:50 So then this will also be 0.
00:53 Okay, so i have in the terminate form, 0 divided by 0...
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