Find lim_(x rarr oo)(4x^(2)-3x)/(x^(3)). Choose 1 answer: (A) 4 (B) 0 (C) -3 (D) The limit is unbounded

Analyze degrees of polynomials: To find the limit of the function as x approaches infinity, we can analyze the degrees of the polynomials in the numerator and the denominator.Degree of numerator and denominator: The degree of the polynomial in the numerator is 2 (because of the term 4x^2), and the degree of the polynomial in the denominator is 3 (because of the term x^3).Comparison of degrees: Since the degree of the denominator is higher than the degree of the numerator, the limit of the function as x approaches infinity is 0. This is because as x becomes very large, the x^3 term in the denominator will grow much faster than the 4x^2 term in the numerator, causing the fraction to approach 0.Limit as x approaches infinity: Therefore, the limit of (4x^2 - 3x) / x^3 as x approaches infinity is 0.

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Find derivatives of logarithmic functions

Full solution

Q. Find

\lim _{x \rightarrow \infty} \frac{4 x^{2}-3 x}{x^{3}}

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Choose

1

answer:

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(A)

4

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(B)

0

\newline

(C)

-3

\newline

(D) The limit is unbounded

Analyze degrees of polynomials: To find the limit of the function as $x$ approaches infinity, we can analyze the degrees of the polynomials in the numerator and the denominator.
Degree of numerator and denominator: The degree of the polynomial in the numerator is $2$ (because of the term $4x^2$ ), and the degree of the polynomial in the denominator is $3$ (because of the term $x^3$ ).
Comparison of degrees: Since the degree of the denominator is higher than the degree of the numerator, the limit of the function as $x$ approaches infinity is $0$ . This is because as $x$ becomes very large, the $x^3$ term in the denominator will grow much faster than the $4x^2$ term in the numerator, causing the fraction to approach $0$ .
Limit as $x$ approaches infinity: Therefore, the limit of $(4x^2 - 3x) / x^3$ as $x$ approaches infinity is $0$ .