Question

How do you calculate this limit without using l’Hospital’s rule: lim (3x^5 + 4x^4 - 3x -2) / (7x^3 - 2x + 5) as x → ∞ ?

Answer 1

See below

Explanation:

`lim_(xtooo)(3x^5+4x^4-3x-2)/(7x^3-2x+5)`

A common way to calculate this limit is dividing all terms by the term of highest degree

`lim_(xtooo)(3x^5/x^5+4x^4/x^5-3x/x^5-2/x^5)/(7x^3/x^5-2x/x^5+5/x^5)=lim_(xtooo)(3+4/x-3/x^2-2/x^5)/(7/x^2-2/x^4+5/x^5)=(3+0-0-0)/(0-0+0)=3/0to oo`