asymptotes of e^x/x
Let's find the asymptotes of exx, for real x
The function is defined on ℝ \ {0}: a vertical asymptote can only be at a finite bound of this domain
As x approaches 0 from the left, the function tends to -∞; from the right, to +∞
The function tends to infinity: the line x = 0 is a vertical asymptote
As x tends to -∞, the function tends to 0: the line y = 0 is a horizontal asymptote at -∞
As x tends to +∞, the function tends to +∞ and f(x)x tends to +∞: no horizontal or slant asymptote at +∞
▶Asymptotes:   { x = 0, y = 0 }
🖼/draw?f1=e%5Ex%2Fx&v=x&x2=0&f3=0&b=-10.0&e=10.0&min=-37.336409243801725&max=409.8884899823993&dash=2,3