Question

let $a(x)=\begin{cases}3 - 6x&x>1\\-1&x = 1\\x^{2}&x<1end{cases}$. find the limit as x approaches $1^{+}$

Explanation:

Step1: Identify the correct - part of the piece - wise function

When finding the limit as $x$ approaches $1^{+}$ (from the right - hand side), we use the part of the piece - wise function where $x>1$. The function for $x > 1$ is $a(x)=3 - 6x$.

Step2: Substitute the value of $x$ into the function

We substitute $x = 1$ into $y=3 - 6x$. So, $\lim_{x
ightarrow1^{+}}a(x)=\lim_{x
ightarrow1^{+}}(3 - 6x)$.
Using the limit rules for polynomial functions, we have $3-6\times1$.
$3-6=-3$.

Answer:

C. -3