`lim_(x to -1) (x^(8)+x^(4)-2)/(x-5)`

Answer

To solve the limit \( \lim_{x \to -1} \frac{x^8 + x^4 - 2}{x - 5} \), we will follow these steps:

### Step 1: Substitute \( x = -1 \) into the function
We start by substituting \( x = -1 \) into the expression:

\[ \frac{(-1)^8 + (-1)^4 - 2}{-1 - 5} \]

### Step 2: Calculate the numerator
Now, we calculate the numerator:

\[ (-1)^8 = 1, \quad (-1)^4 = 1 \]
Thus, the numerator becomes:

\[ 1 + 1 - 2 = 0 \]

### Step 3: Calculate the denominator
Next, we calculate the denominator:

\[ -1 - 5 = -6 \]

### Step 4: Form the limit expression
Now we can form the limit expression:

\[ \frac{0}{-6} = 0 \]

### Step 5: Conclude the limit
Since we have obtained a finite value, we conclude that:

\[ \lim_{x \to -1} \frac{x^8 + x^4 - 2}{x - 5} = 0 \]

### Final Answer
Thus, the limit is:

\[ \boxed{0} \]

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