Question

for the function f(x) shown below, determine \\(\lim_{x\to - 1^{-}}f(x).

f(x)=\

$$\begin{cases}-2 - 2x^{2}&\\text{for }xleq - 1\\4x + 10&\\text{for }x > - 1\\end{cases}$$

answer attempt 1 out of 2

dne

Explanation:

Step1: Identify the correct - part of the function

Since we are finding $\lim_{x
ightarrow - 1^{-}}f(x)$, we use the part of the function where $x\leq - 1$. The function for $x\leq - 1$ is $f(x)=-2 - 2x^{2}$.

Step2: Substitute $x=-1$ into the function

Substitute $x = - 1$ into $y=-2 - 2x^{2}$. We get $y=-2-2(-1)^{2}$.

Step3: Calculate the result

First, calculate $(-1)^{2}=1$. Then $2(-1)^{2}=2$. So $y=-2 - 2=-4$.

Answer:

$-4$