Question

How do you find the limit of `(4x^2 -3x+2)/(7x^2 +2x-1)` as x approaches infinity?

Answer 1

`4/7`

Explanation:

divide numerator and denominator by the highest exponent of x , in this case `x^2`

hence `( (4x^2)/x^2 - (3x)/x^2 + 2/x^2)/((7x^2)/x^2 + (2x)/x^2 - 1/x^2)`

`= (4 - 3/x +2/x^2)/(7 + 2/x -1/x^2)`

`rArr lim_(x→∞) f(x) = 4/7` graph{(4x^2-3x+2)/(7x^2+2x-1) [-5.07, 5.067, -2.526, 2.54]}