precalculus 2.2 ws limits of polynomials\nname: rosene jenny mistok\nuse the following functions to evaluate…

precalculus 2.2 ws limits of polynomials\nname: rosene jenny mistok\nuse the following functions to evaluate the limits. sketch a graph to help if needed.\n$f(x)=x^{3}-2x^{2}+4x$\n$g(x)=-3x^{4}+2x$\n1. $limlimits_{x\to-infty}f(x)=$\n2. $limlimits_{x\toinfty}g(x)=$\n3. $limlimits_{x\toinfty}f(x)=$\nevaluate the limit\n4. $limlimits_{x\to-infty}5x^{2}-3x + 1=$\n5. $limlimits_{x\toinfty}-x^{5}+9=$\n6. $limlimits_{x\to-infty}2x - 3=$

Answer

Explanation:

Step1: Analyze the leading term of (f(x)=x^{3}-2x^{2}+4x)

For (x\to-\infty), the leading term is (x^{3}). As (x\to-\infty), (x^{3}\to-\infty). So (\lim_{x\to-\infty}f(x)=-\infty)

Step2: Analyze the leading term of (g(x)=-3x^{4}+2x)

For (x\to\infty), the leading term is (-3x^{4}). As (x\to\infty), (x^{4}\to\infty) and (-3x^{4}\to-\infty). So (\lim_{x\to\infty}g(x)=-\infty)

Step3: Analyze the leading term of (f(x)=x^{3}-2x^{2}+4x)

For (x\to\infty), the leading term is (x^{3}). As (x\to\infty), (x^{3}\to\infty). So (\lim_{x\to\infty}f(x)=\infty)

Step4: Analyze the leading term of (y = 5x^{2}-3x + 1)

For (x\to-\infty), the leading term is (5x^{2}). As (x\to-\infty), (x^{2}\to\infty) and (5x^{2}\to\infty). So (\lim_{x\to-\infty}(5x^{2}-3x + 1)=\infty)

Step5: Analyze the leading term of (y=-x^{5}+9)

For (x\to\infty), the leading term is (-x^{5}). As (x\to\infty), (x^{5}\to\infty) and (-x^{5}\to-\infty). So (\lim_{x\to\infty}(-x^{5}+9)=-\infty)

Step6: Analyze the function (y = 2x-3)

For (x\to-\infty), as (x\to-\infty), (2x\to-\infty). So (\lim_{x\to-\infty}(2x - 3)=-\infty)

Answer:

(-\infty)
(-\infty)
(\infty)
(\infty)
(-\infty)
(-\infty)