Answered

Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.