`lim_(x->(1/2)) (6x^2 + 5x - 4)/(4x^2 + 16x - 9)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s...

`lim_(x->(1/2)) (6x^2 + 5x - 4)/(4x^2 + 16x - 9)` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

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Chapter 4, 4.4 - Problem 10 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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`lim_(x->1/2)(6x^2+5x-4)/(4x^2+16x-9)`

`=lim_(x->1/2)((2x-1)(3x+4))/((2x-1)(2x+9))`

`=lim_(x->1/2)(3x+4)/(2x+9)`

plug in the value,

`=(3*1/2+4)/(2*1/2+9)`

`=(3+8)/(2+18)=11/20`

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