# If limx-->a f(x)= ∞ and limx-->g(x)=c, where c is a real number. Prove a)limx-->[f(x)+g(x)]= ∞ b)limx-->a[f(x)g(x)]= ∞ if c>0

### 1 Answer | Add Yours

Here we need to memorize some of the properties of algebraic limit theorem.

`lim_(xrarra)[f(x)+g(x)] = lim_(xrarra) f(x)+lim_(xrarra) g(x)`

`lim_(xrarra)[f(x)*g(x)] = lim_(xrarra) f(x)*lim_(xrarra) g(x)`

So if we apply this in to our question;

`lim_(xrarra)[f(x)+g(x)] `

`= lim_(xrarra) f(x)+lim_(xrarra) g(x)`

`= oo+c`

`= oo`

`lim_(xrarra)[f(x)*g(x)] `

`= lim_(xrarra) f(x)*lim_(xrarra) g(x)`

`= oo*c`

= `oo` *{since c>0. If c<0 it will become `-oo` }*

oo is the number without limit. So it is the largest possible number we have.

So if we add c to infinity; `c+oo = oo`

Even we multiply c by infinity; `c*oo = oo`

**Sources:**