Drive formula for quotient rule of differentiation -

Question

1. Prove that ∀ a∈N, ∀b∈N, ∀c∈N, a≡n b→ca ≡n cb

2. Find lim(x→ ∞)(x + ³√(1 - x³ ))

3. Prove by mathematical induction that any integer amount of 18 dollars or higher can be expressed as a combination of 3 dollar and 10 dollar bills.

4. Prove quotient rule of limits.

5. Prove ∑_(i=1)ⁿ i.2ⁱ = (n-1)2⁽ⁿ⁺¹⁾ + 2

6. Derive formula for quotient rule of differentiation.