Find the value of `lim_(x->oo)(2x^2 - 9x)/(4x^3 + x - 7)` using L'Hopital's rule

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We have determine: `lim_(x->oo)(2x^2 - 9x)/(4x^3 + x - 7)`

If we substitute x = inf. in the expression, both the numerator and the denominator are equal to inf. As ` `inf./inf. is indeterminate we can use l'Hopital's rule and substitute the numerator and the denominator with their derivatives.

=> `lim_(x->oo)(4x - 9)/(12x^2 + 1)`

Again, we see that substituting x with inf. gives the indefinite form inf./inf. The numerator and denominator are substitute by their derivatives again

=> `lim_(x->oo) 4/(24x)`

When x tends to inf. 1/6x tends to 0.

The value of `lim_(x->oo)(2x^2 - 9x)/(4x^3 + x - 7) = 0`

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