Find the limit use ihospitals rule if appropriate if there

Question

1. Find the limit. Use I'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

lim_x→0⁺ (tan 5x)^x.

2. Find the limit. Use I'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

lim_x→0 (1 - 8x)^1/x.

3. Find the limit. Use I'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.

lim_x→∞ (1 + a/x)^bx.