Assume a, b, c, d, and e are non-zero constants. Compute the limit algebraically:
a) lim (x → 0) (ax² + bx + c) / (dx + e)
b) lim (x → [infinity]) (ax³ + bx² + cx + d) / (ex²)
c) lim (x → 1) (a√x + b) / (c√x + d)
d) lim (x → -[infinity]) (ax² - bx + c) / (dx - e)