My Math Forum confused about a limit question

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 May 8th, 2010, 07:20 PM #1 Member   Joined: Sep 2009 Posts: 43 Thanks: 0 confused about a limit question Given that lim x->c f(x)=6 and that lim x->c g(x)= -4, evaluate the following limit. Assume that c is a constant. The x in front of the f is confusing me. lim [xf(x) + 3 g(x)]^2 x->c
 May 8th, 2010, 07:45 PM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: confused about a limit question Your answer should have "c" in it (at least once)... does that give you some confidence moving forward?
 May 9th, 2010, 12:50 PM #3 Senior Member   Joined: Jan 2009 Posts: 345 Thanks: 3 Re: confused about a limit question $\lim_{x\to c}f[x]=6$ and $\lim_{x\to c} g[x]=5$ $\text \lim_{x\to c} (xf(x) + 3 g(x))^{2} \Rightarrow \lim_{x\to c} [x^{2}(f(x))^{2} +6(xf(x)g(x))+9(g(x))^{2}]$ expanding the limits $\lim_{x\to c} x^{2}(f(x))^{2} + 6( \lim_{x\to c} (xf(x)g(x)))+9(\lim_{x\to c}(g(x))^{2})= c^{2}(36 + 6c*180)+ 9*25$ hope this helps
May 9th, 2010, 12:52 PM   #4
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Re: confused about a limit question

Quote:
 Originally Posted by alevis ... $\lim_{x\to c} x^{2}(f(x))^{2} + 6( \lim_{x\to c} (xf(x)g(x)))+9(\lim_{x\to c}(g(x))^{2})= c^{2}(36 + 6c*180)+ 9*25$ hope this helps
This is not correct.

 May 9th, 2010, 02:10 PM #5 Senior Member   Joined: Apr 2010 Posts: 215 Thanks: 0 Re: confused about a limit question $\lim_{n \rightarrow c} (x f(x) + 3 g(x))^2= x^2f(x)^2 + 9g(x)^2 + 6xf(x)g(x)$ $= c^2 6^2 + 9*2^5 + 6c*6*5$ $= 36c^2 + 180c + 225$
May 18th, 2010, 04:21 PM   #6
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Re: confused about a limit question

Quote:
 Originally Posted by brangelito $\lim_{n \rightarrow c} (x f(x) + 3 g(x))^2= x^2f(x)^2 + 9g(x)^2 + 6xf(x)g(x)$ $= c^2 6^2 + 9*2^5 + 6c*6*5$ $= 36c^2 + 180c + 225$
Thanks for the correction

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