R rowdy3 Apr 2008 80 2 May 8, 2010 #1 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

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

slovakiamaths Apr 2010 41 15 India May 8, 2010 #2 \(\displaystyle \lim_{x\rightarrow{c}}(xf(x)+3g(x))^2=\lim_{x\rightarrow{c}}[x^2f^2(x)+9g^2(x)+6xf(x)g(x)] =c^2(6)^2+9(-4)^2+6c(6)(-4)\) \(\displaystyle =36c^2+144-144c\)

\(\displaystyle \lim_{x\rightarrow{c}}(xf(x)+3g(x))^2=\lim_{x\rightarrow{c}}[x^2f^2(x)+9g^2(x)+6xf(x)g(x)] =c^2(6)^2+9(-4)^2+6c(6)(-4)\) \(\displaystyle =36c^2+144-144c\)