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anonymous
 one year ago
Find the indicated limit, if it exists. lim x>0 f(x), f(x)=(9x^2, x<0, 9, x=0, 4x+9, x>0)
anonymous
 one year ago
Find the indicated limit, if it exists. lim x>0 f(x), f(x)=(9x^2, x<0, 9, x=0, 4x+9, x>0)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Choices are The limit does not exist, 9, 4, 13

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, we can see that the function value at 0 is equal to 9, but that doesn't mean the limit is 9. We want to show that the limit as x approaches zero from the left is equal to the limit as we approach zero from the right. Since f is definited to be 9x^2 for x < 0, we follow the path along f = 9x^2 as we approach from the left. So taking that limit: \[\lim_{x \rightarrow 0^{}}(9x^{2}) = 90 = 9\] If we approach from the right, then we're approaching along the path f = 4x + 9. So th limit from the right uses this function and we have: \[\lim_{x \rightarrow 0^{+}}(4x+9) = 0 + 9 = 9\] Thus the limit from the left is equal to the limit from the right and that value is equal to 9.
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