**1. Additive Method**

Under this method, the limit of the sum of any two, or more function say f(X) and g(x) is determined by the following model.

Lim [f(x) ± g(x)] = lim f(x) ± lim g(x)

x→ a x → a x → a

**Example**

**Limit **(** **x² + 2x + 5 ) = lim x² + lim 2x + lim 5

x→ 0 x→ 0 x→ 0

= 0^{2} + 2 × 0 + 5 = 5

**2. Multiplicative Method**

Under this method, the limit of the product of any two, or more functions say f(x) and f(g) is computed by the following model:

Lim [f(x) . g(x)] = lim f(x) . lim g(x)

x→ a x → a x → a

**Example **

Lim (x-4) (x + 5) = lim (x – 4) × lim (x + 5)

x→ 3 x→ 3

= (3 – 4) × (3 + 5) = -8

**3. Constantive Method**

Under this method, the limit of the product of a constant say K, and a function say f(x) is determined by the following model:

Lim K. f(x) = K lim f(x)

x→ a x → a

**Example**

Lim 5 x 3 + 3 x 2 – 2x = lim 5 x 3 + lim 3 x 2 – lim 2x

x→ 2 x → 2 x → a

= 5 × 2^{3} + 3 × 2^{2 }– 2 × 2 = 48

**4. Dividing Method**

Under this method, the limit of the quotient of any two functions say f(x), and g(x) is determined by the following model: