Answered

Find expert answers and community support for all your questions on IDNLearn.com. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.

find the horizontal asymptote for y= 5x/x+6 .
y = 0
y = −6
none
y = 5

Sagot :

Semsee45idn

Answer:

[tex]y = 5[/tex]

Step-by-step explanation:

Given function:

[tex]y=\dfrac{5x}{x+6}[/tex]

[tex]\implies y=5 \left( \dfrac{x}{x+6}\right)[/tex]

[tex]\textsf{As }x \rightarrow +\infty, \ \dfrac{x}{x+6} \rightarrow1[/tex]  

[tex]\implies y\rightarrow5[/tex]

[tex]\textsf{As }x \rightarrow -\infty, \ \dfrac{x}{x+6} \rightarrow1[/tex]  

[tex]\implies y\rightarrow5[/tex]

As [tex]x[/tex] approaches infinity and negative infinity, [tex]y[/tex] approaches 5 (but never gets there).    Therefore, the horizontal asymptote is [tex]y=5[/tex]

We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.