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Help with AP Calculus?
1. Find the limit as x approaches infinity for e^2x-1.
2. Find a quadratic function q(x) such that f(x)=(x^2-4)/q(x) has one horizontal asymptote y=-1/2 and exactly one vertical asymptote x=3.
1 Answer
- Lv 79 years agoFavorite Answer
I can only offer help in the 2nd question.
horizontal asymptote = end behavior as x approaches infinity. As x gets really large, only the bigger orders matter since the small numerical values like 4 are essentially negligible.
So you need -2x^2 in the denominator.
For the vertical asymptote at x = 3, you need a quadratic equation such that x cannot be equal to 3 at any value of f(x). This is achievable only by making the equation equal to some undefined value at x equals 3. To do this, put in a (x-3)^2 in the denominator.
For the question #1, I think the answer is infinity but I'm not entirely sure.
