Question

for the function f(x) shown below, determine lim f(x) as x→1. f(x) = { -x² + 5 for x > 1; -4x + 10 for x ≤ 1 } answer attempt 1 out of 2 dne

Explanation:

Step1: Find left - hand limit

We use the part of the function for $x\leq1$. Substitute $x = 1$ into $y=-4x + 10$.
$y=-4\times1 + 10=6$

Step2: Find right - hand limit

We use the part of the function for $x>1$. Substitute $x = 1$ into $y=-x^{2}+5$.
$y=-1^{2}+5=4$

Step3: Check if limit exists

Since the left - hand limit ($6$) is not equal to the right - hand limit ($4$), the limit does not exist.

Answer:

DNE