Questions: Find the limit (if it exists). lim x→1− f(x), where f(x)= x^3+3, x<1 x+3, x≥1 3 0 Limit does not exist. 4 9

Transcript text: Find the limit (if it exists). \[ \lim _{x \rightarrow 1^{-}} f(x), \text { where } f(x)=\left\{\begin{array}{rr} x^{3}+3, & x<1 \\ x+3, & x \geq 1 \end{array}\right. \] 3 0 Limit does not exist. 4 9

Solution

Solution Steps

To find the limit of \( f(x) \) as \( x \) approaches 1 from the left (\( x \rightarrow 1^{-} \)), we need to consider the expression for \( f(x) \) when \( x < 1 \). In this case, \( f(x) = x^3 + 3 \). We will substitute \( x = 1 \) into this expression to find the limit.

Step 1: Identify the Relevant Expression for \( x < 1 \)

To find the limit of \( f(x) \) as \( x \rightarrow 1^{-} \), we consider the expression for \( f(x) \) when \( x < 1 \). The function is given by: \[ f(x) = x^3 + 3 \]

Step 2: Substitute \( x = 1 \) into the Expression

We substitute \( x = 1 \) into the expression \( f(x) = x^3 + 3 \) to find the limit: \[ f(1) = 1^3 + 3 = 4 \]