Question

Given the following piecewise function, evaluate lim

x→1
​
f(x). (If the limit does not exist, enter Ø.) f(x)=
⎩
⎨
⎧
​

2x
2
−3x−2
−2x
2
+3x−2
−2x
2
−1
​

if x≤−4
if −4 if x>1
​

Answer 1

Step-by-step explanation: To evaluate the limit as x approaches 1 for the given piecewise function, we need to consider the right-hand limit and the left-hand limit separately.

Right-hand limit (x → 1+):

For x > 1, the function is defined as -2x^2 + 3x - 2.

Substituting x = 1 into the function: -2(1)^2 + 3(1) - 2 = -1.

Left-hand limit (x → 1-):

For x ≤ -4, the function is defined as 2x^2 - 3x - 2.

Since x = 1 is not within the specified range, we cannot evaluate the left-hand limit at x = 1.

Since the right-hand limit (-1) is defined, but the left-hand limit is not defined for x = 1, the limit as x approaches 1 for the given function does not exist (Ø).