# What is the best way to solve problem like these ↓ ? (Limits to infinity)

##
Problems such as

When #x# approaches positive infinity, find the limit of

#(3x-1)/(sqrt(x^2-6#

#(sqrt(4x^2+4x))/(4x+1)#

I know that you can solve by substituting values of #x# as it gets closer to infinity, but is there a way to solve, like factorising, formula, or a general rule?

Problems such as

When

I know that you can solve by substituting values of

##### 1 Answer

Jun 22, 2017

As a general rule convert a polynomial

(A)

#### Explanation:

- let us divide numerator and denominator by
#x# and we get

=

graph{(3x-1)/sqrt(x^2-6) [2.07, 19.55, -0.37, 8.37]}

- dividing numerator and denominator by
#2x# and we get

=

graph{sqrt(4x^2+4x)/(4x+1) [-0.152, 4.218, -0.51, 1.675]}

As a general rule convert a polynomial