let $a(x)=\begin{cases}3 - 6x&x>1\\-1&x = 1\\x^{2}&x<1end{cases}$. find the limit as x approaches $1^{+}$
let $a(x)=\begin{cases}3 - 6x&x>1\\-1&x = 1\\x^{2}&x<1end{cases}$. find the limit as x approaches $1^{+}$
Answer
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, $\lim_{x\rightarrow1^{+}}a(x)=\lim_{x\rightarrow1^{+}}(3 - 6x)$. Using the limit rules for polynomial functions, we have $3-6\times1$. $3-6=-3$.
Answer:
C. -3