Find the asymptotes of the Parametric equation? Consider x(t)=2e^(−t)+3e^(2t) y(t)=5e^(−t)+2e^(2t) which represents a non rectilinear paths Horizontal and Verical Asymptotes : If t-> + infinity or − infty , then x(t) and y(t) -> infty, So there are no asymptotes parallel to coordinate axis oblique Asymptotes: Please tell me how to find the Oblique asymptotes

Madison Costa

Madison Costa

Answered question

2022-11-05

Find the asymptotes of the Parametric equation?
Consider
x ( t ) = 2 e t + 3 e 2 t
y ( t ) = 5 e t + 2 e 2 t
which represents a non rectilinear paths
Horizontal and Verical Asymptotes :
If t +     o r     and x ( t )     a n d     y ( t )     , So there are no asymptotes parallel to coordinate axis
oblique Asymptotes:
Please tell me how to find the Oblique asymptotes

Answer & Explanation

Eynardfb0

Eynardfb0

Beginner2022-11-06Added 19 answers

There are two asymptotes by inspection which are at an angle to x-axis.
We need to find out not y ( t ) x ( t ) ) tendency but tendency of limits of oblique asymptotes.
d y / d t d x / d t when t +
and also
d y / d t d x / d t when t
separately.
These limits evaluate to 5/2 and 2/3 for each asymptote as coefficients for positive and negative exponents.
Better to make parametric plot of the curve and an ordinary plot of the slope.

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