Question

question 15
if $lim_{x \to 4} f(x)=3$, and $lim_{x \to 4} g(x)= - 1$, then find $lim_{x \to 4}3g(x)-f(x)$.
-3
-6
3
no correct answer choice is given.

Explanation:

Step1: Apply limit - sum and constant - multiple rules

By the sum rule of limits $\lim_{x
ightarrow a}[u(x)\pm v(x)]=\lim_{x
ightarrow a}u(x)\pm\lim_{x
ightarrow a}v(x)$ and the constant - multiple rule $\lim_{x
ightarrow a}[c\cdot u(x)] = c\cdot\lim_{x
ightarrow a}u(x)$, we have $\lim_{x
ightarrow4}[3g(x)-f(x)]=3\lim_{x
ightarrow4}g(x)-\lim_{x
ightarrow4}f(x)$.

Step2: Substitute the given limit values

Given $\lim_{x
ightarrow4}f(x) = 3$ and $\lim_{x
ightarrow4}g(x)=-1$. Substitute these values into the expression: $3\times(-1)-3$.

Step3: Calculate the result

$3\times(-1)-3=-3 - 3=-6$.

Answer:

$-6$