Use L'Hospital Rule to evaluate \lim_{x\to\infty}\frac{2x^2+3x}{2x^3+3x+7}

Chaya Galloway

Chaya Galloway

Answered question

2021-10-22

Use L'Hospital Rule to evaluate limx2x2+3x2x3+3x+7, Then determine the limit using limit laws and commonly known limits.

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-10-23Added 96 answers

Given limx2x2+3x2x3+3x+7
Apply LHopital rule
=limxddx(2x2+3x)ddx(2x3+3x+7)
=limx(4x+3)6x2+3
again Apply Lhopital rule
=limxddx(21x+3)ddx(6x2+3)
=limx46x
plug x==46(1)
=0
finally limx2x2+3x2x3+3x+7=0
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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