Find the following using L'Hospital's rule
`(i) lim_(xto0) ((16+5x)^(1//4)-2)/((32+3x)^(1//5)-2)" "(ii)lim_(xto pi//2) [xtanx-(pi//2)secx]`

Explanation

Let's solve the given limits step by step using L'Hospital's Rule.

### Part (i):
Find \( \lim_{x \to 0} \frac{(16 + 5x)^{1/4} - 2}{(32 + 3x)^{1/5} - 2} \).

**Step 1: Check for indeterminate form**
Substituting \( x = 0 \):
- Numerator: \( (16 + 5 \cdot 0)^{1/4} - 2 = 2 - 2 = 0 \)
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