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

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- May 8th 2010, 07:18 PMrowdy3Im confuse 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, 07:34 PMslovakiamaths
$\displaystyle \lim_{x\rightarrow{c}}(xf(x)+3g(x))^2=\lim_{x\righ tarrow{c}}[x^2f^2(x)+9g^2(x)+6xf(x)g(x)]

=c^2(6)^2+9(-4)^2+6c(6)(-4)$

$\displaystyle =36c^2+144-144c$