Questions: Solve for Amit lim (x -> -2) (x-5)/(6x^2-4x+8)

Transcript text: Solve for Amit \[ \lim _{x \rightarrow-2} \frac{x-5}{6 x^{2}-4 x+8} \]

Solution

Solution Steps

To solve the limit problem, we need to evaluate the expression as \( x \) approaches \(-2\). First, check if direct substitution results in an indeterminate form. If it does, consider simplifying the expression or using L'Hôpital's Rule if applicable.

Step 1: Evaluate the Limit Expression

To find the limit of the function as \( x \) approaches \(-2\), we start with the expression:

\[ \lim _{x \rightarrow-2} \frac{x-5}{6x^{2}-4x+8} \]

Step 2: Check for Indeterminate Form

Substitute \( x = -2 \) directly into the expression:

\[ \frac{-2-5}{6(-2)^{2}-4(-2)+8} = \frac{-7}{24+8+8} = \frac{-7}{40} \]

Since the substitution does not result in an indeterminate form, we can directly evaluate the limit.