Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

The expression defining each function consists of a sum or difference of terms and, as written, the long-term behavior of each function is an indeterminate form (an expression which does not have a defined value without additional information) of the type “∞ - ∞”. Find the long-term behavior of each function by first writing each as a ratio of two polynomials.

The Expression Defining Each Function Consists Of A Sum Or Difference Of Terms And As Written The Longterm Behavior Of Each Function Is An Indeterminate Form An class=

Sagot :

Given function is

[tex]y(t)=\frac{t^2+t}{t+2}-\frac{t^3}{t+3}[/tex]

The lease common multiple of (t+2) and (t+3) is (t+2)(t+3) , making the denominator (t+2)(t+3).

[tex]y(t)=\frac{(t^2+t)(t+3)}{(t+2)(t+3)_{}}-\frac{t^3(t+2)}{(t+3)(t+2)}[/tex]

[tex]y(t)=\frac{t^2(t+3)+t(t+3)}{(t+2)(t+3)_{}}-\frac{t^3(t+2)}{(t+3)(t+2)}[/tex]

[tex]y(t)=\frac{t^3+3t^2+t^2+3t}{(t+2)(t+3)_{}}-\frac{t^4+2t^3}{(t+3)(t+2)}[/tex]

[tex]y(t)=\frac{t^3+4t^2+3t-t^4-2t^3}{t\mleft(t+3\mright)+2\mleft(t+3\mright)_{}}[/tex]

[tex]y(t)=\frac{-t^4-t^3+4t^2+3t}{t^2+3t+2t+6_{}}[/tex]

[tex]y(t)=\frac{-t^4-t^3+4t^2+3t}{t^2+5t+6_{}}[/tex]

Hence the ratio of two polynomial is

[tex]y(t)=\frac{-t^4-t^3+4t^2+3t}{t^2+5t+6_{}}[/tex]

The long term behavior is

[tex]y(t)=\frac{-t^4-t^3+4t^2+3t}{t^2+5t+6_{}}\approx\frac{-t^4}{t^2}=-t^2[/tex][tex]\text{ So x }\rightarrow\pm\infty\text{ y likes like y}=-x^2[/tex][tex]\lim _{n\to\infty}-t^2=-\infty[/tex]

[tex]\lim _{n\to-\infty}-t^2=-\infty[/tex]

The is not a horizontal line, So this is not horizontal asymptotes.

Hence the asymptotes is oblique.

View image EdwarM364612
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.