Question

question 4 - 1 point given that lim(x→1) f(x)= - 4 and lim(x→1) g(x)=1, use the limit laws to evaluate lim(x→1) (3f(x)+9g(x)). provide your answer below:

Explanation:

Step1: Apply limit - sum law

$\lim_{x
ightarrow1}(3f(x)+9g(x))=\lim_{x
ightarrow1}(3f(x))+\lim_{x
ightarrow1}(9g(x))$

Step2: Apply limit - constant - multiple law

$\lim_{x
ightarrow1}(3f(x)) = 3\lim_{x
ightarrow1}f(x)$ and $\lim_{x
ightarrow1}(9g(x))=9\lim_{x
ightarrow1}g(x)$

Step3: Substitute given limits

Since $\lim_{x
ightarrow1}f(x)= - 4$ and $\lim_{x
ightarrow1}g(x)=1$, we have $3\lim_{x
ightarrow1}f(x)+9\lim_{x
ightarrow1}g(x)=3\times(-4)+9\times1$

Step4: Calculate the result

$3\times(-4)+9\times1=-12 + 9=-3$

Answer:

$-3$