Evaluate `lim_(xto2) (x^(10)-1024)/(x^(5)-32).`

Explanation

To evaluate the limit \( \lim_{x \to 2} \frac{x^{10} - 1024}{x^{5} - 32} \), we can follow these steps:

### Step 1: Rewrite the expression
Recognize that \( 1024 = 2^{10} \) and \( 32 = 2^{5} \). Thus, we can rewrite the limit as:
\[ \lim_{x \to 2} \frac{x^{10} - 2^{10}}{x^{5} - 2^{5}} \]

...