Question

Find the limit. (If an answer does not exist, enter DNE.) \\ $\lim_{x \to 0} \frac{\sin 9x}{x}$

          Find the limit. (If an answer does not exist, enter DNE.) \\
$\lim_{x \to 0} \frac{\sin 9x}{x}$
        
Find the limit. (If an answer does not exist, enter DNE.) 

limx → 0(sin 9x)/(x)

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Find the limit. (If an answer does not exist, enter DNE.) lim_(x->0)(sin(9x))/(x)
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Transcript

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00:01 The quick answer to this problem, the limit as x approaches 0, of what do we get, sign of 3x over sign of 8x, is that the correct answer is 3 eighths.
00:19 Now, one way that you could do this is you can rewrite this limit.
00:24 So the limit as x approaches 0 is i could leave the sign of 3x in there, as well as sign of 3x in there, as well as sign of, of 8x in there and then what i could do is multiply the top and the bottom by something.
00:43 So what i could do is multiply the bottom by 3x if i also multiply the top by 3x, but i'm also going to multiply the top by 8 and the bottom, that's not what i wanted, and the bottom by 8...
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