Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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

Sagot :

semsee45

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]

Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.