# How do you find the limit of #1/(x^3 +4)# as x approaches #oo#?

# lim_(x rarr oo) 1/(x^3+4) = 0 #

graph{ 1/(x^3+4) [-7, 13, -4.16, 5.84]}

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To find the limit of 1/(x^3 + 4) as x approaches infinity, we can observe that as x becomes larger and larger, the term x^3 dominates the denominator. Therefore, we can approximate the expression by ignoring the constant term 4 and considering only the term x^3.

As x approaches infinity, x^3 also approaches infinity. Thus, the denominator becomes very large, and as a result, the fraction 1/(x^3 + 4) approaches zero.

Therefore, the limit of 1/(x^3 + 4) as x approaches infinity is 0.

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To find the limit of ( \frac{1}{x^3 + 4} ) as ( x ) approaches infinity (( \infty )), you compare the rates at which the numerator and the denominator grow. As ( x ) becomes very large, the ( x^3 ) term in the denominator grows much faster than the constant term ( 4 ), and the numerator remains constant at ( 1 ). Therefore, the fraction as a whole approaches ( 0 ) because the denominator becomes infinitely large, making the fraction infinitely small. Mathematically, this is expressed as:

[ \lim_{{x \to \infty}} \frac{1}{x^3 + 4} = 0 ]

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