suppose lim f(x) = 4 and lim g(x) = 6 x→2 x→2...

# Explanation: ## Step1: Apply limit - sum rule $\lim_{x\rightarrow a}(u(x)+v(x))=\lim_{x\rightarrow a}u(x)+\lim_{x\rightarrow a}v(x)$. So, $\lim_{x\rightarrow 2}(- 2f(x)+9g(x))=\lim_{x\rightarrow 2}(-2f(x))+\lim_{x\rightarrow 2}(9g(x))$. ## Step2: Apply limit - constant - multiple rule $\lim_{x\rightarrow a}(cf(x)) = c\lim_{x\rightarrow a}f(x)$. Then $\lim_{x\rightarrow 2}(-2f(x))=-2\lim_{x\rightarrow 2}f(x)$ and $\lim_{x\rightarrow 2}(9g(x)) = 9\lim_{x\rightarrow 2}g(x)$. ## Step3: Substitute given limits We know that $\lim_{x\rightarrow 2}f(x)=4$ and $\lim_{x\rightarrow 2}g(x)=6$. So, $-2\lim_{x\rightarrow 2}f(x)+9\lim_{x\rightarrow 2}g(x)=-2\times4 + 9\times6$. ## Step4: Calculate the result $-2\times4+9\times6=-8 + 54=46$. # Answer: $46$