suppose lim f(x) = 4 and lim g(x) = 6 x→2 x→2 what is lim(-2 f(x)+9 g(x))? 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:

$46$