Solve. lim_(x rarr oo)(root(3)(x^3-2x^2+3)/(2x+1)

Khaleesi Herbert 2021-02-25 Answered
Solve. limx(x32x2+332x+1
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Expert Answer

faldduE
Answered 2021-02-26 Author has 109 answers
limx((x32x2+332x+1)=12
To start, divide by the highest denominator power by using the following algebraic property:
a+b=a(1+ba)
(x32x2+33=(x3(12x+3x3)3
xx33=x
x12x+3x33
=12x+3x332x+1
Then, divide by x and refine:
12x+3x33x/(2x2+1x)
=12x+3x332+1x
Then, take the limit of the numerator and denominator using the limit quotient rule, which is:
limx[(f(x)g(x))]=limxf(x)limxg(x),limxg(x)
lim(x)(12x+3x33)limx(2+1x)
The limit of the numerator is 1:
limx(12x+3x33)
limx(12x+3x3)3
limx(1limx(2x+limx(3x3)))3
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