Find the limit: lim_{xrightarrowinfty}frac{3x^6-x^4+2x^2-3}{4x^5+2x^3-5}

jernplate8 2021-01-02 Answered
Find the limit:
limx3x6x4+2x234x5+2x35
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Expert Answer

Tuthornt
Answered 2021-01-03 Author has 107 answers
limx3x6x4+2x234x5+2x35
Multiply and divided by x5:
limx3x6x4+2x234x5+2x35=limxx53x6x4+2x23x5x54x5+2x35x5
Divide:
limxx53x6x4+2x23x5x54x5+2x35x5=limx3x1x+2x33x54+2x25x5
The limit of the quotient is the quotient of limits:
limx3x1x+2x33x54+2x25x5=limx(3x1x+2x33x5)limx(4+2x25x5)
The limit of a sum/difference is the sum/difference of limits: limx(3x1x+2x33x5)limx(4+2x25x5)=(limx3x5+limx2x3limx1x+limx3x)limx(4+2x25x5)
The limit of a quotient is the quotient of limits:
(limx3x5+limx2x3limx1x+limx3x)limx(4+2x25x5)=(limx3x5+limx2x3limx3x)limx1limxxlimx(4+2x25x5)
The limit of a constant is equal to the constant:

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