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find the vertical and horizontal asymptotes?
Find all the vertical and horizontal asymptotes of the function f , justify with limits.
f(x)= (3e^(x))/(2-2e^(x))
1 Answer
- Jeff AaronLv 76 years agoFavorite Answer
Vertical asymptote: where the denominator is zero:
2 - 2e^x = 0
2e^x = 2
e^x = 2/2
e^x = 1
x = ln(1)
x = 0
Horizontal asymptote #1:
As x approaches positive infinity, e^x, approaches positive infinity, the in the denominator the 2 becomes insignificant as compared to the -2e^x, so we're left with:
f(x) = (3e^x) / (-2e^x) = -3/2 = -1.5
Horizontal asymptote #2:
As x approaches negative infinity, e^x approaches zero, so we're left with:
f(x) = (3*0) / (2 - 2*0)
f(x) = 0 / (2 - 0)
f(x) = 0/2
f(x) = 0
