Question

Find the asymptotes of the curve y = e^x

Answer 1

The given equation of the curve is y = e^x .

(a) For Asymptotes Parallel to X-axis 

let x → ±∞, then (i) x → ∞ implies y → ∞ 

(ii) x → –∞ implies y → 0(= e ^{– ∞}) Hence as per definition, y = 0 (for x → –∞) is an asymptote parallel to X-axis

(b) For Asymptote Parallel to Y-axis 

Rewrite the given equation as x = log y and let y → ±∞. Now in the case for y → ±∞, x does not tend to any finite value. Whence there is no asymptote parallel to Y-axis.

(c) Oblique Asymptote:

 (No finite value), hence no oblique asymptote (L' Hospital Rule).