Limits at Infinity Worksheet
Explore the behavior of functions as input values approach positive and negative infinity with this Grade 11 Calculus worksheet.
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Limits at Infinity
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Read each question carefully and determine the limits of the given functions as x approaches positive or negative infinity. Show all your work.
1. What is the limit of f(x) = (3x^2 - 2x + 1) / (x^2 + 4x - 5) as x approaches infinity?
0
1
3
infinity
2. Evaluate lim (x→ -∞) [(5x^3 + 2x - 7) / (2x^4 - 3x^2 + 1)]
0
5/2
-7
-infinity
3. If the degree of the numerator is less than the degree of the denominator, the limit of the rational function as x approaches infinity is .
4. If the degrees of the numerator and denominator are equal, the limit of the rational function as x approaches infinity is the ratio of their .
5. Determine the horizontal asymptote(s) of the function f(x) = (4e^x - 1) / (2e^x + 3) as x approaches infinity and negative infinity.
6. Explain the concept of a horizontal asymptote in the context of limits at infinity.
7. The limit of a polynomial function as x approaches infinity is always infinity or negative infinity.
True
False
8. If lim (x→∞) f(x) = L, then the line y = L is a vertical asymptote of f(x).
True
False
9. Consider the graph of a function y = f(x). If the graph approaches the line y = 2 as x approaches positive infinity, what is lim (x→∞) f(x)?