Limits at Infinity Worksheet

Limits at Infinity

Read each question carefully and determine the limit of the given functions as x approaches infinity or negative infinity. Show all your work.

1. When evaluating a limit at infinity for a rational function, we compare the degrees of the numerator and the  .

2. If the degree of the numerator is greater than the degree of the denominator, the limit will be   or negative infinity.

3. If the degree of the denominator is greater than the degree of the numerator, the limit will be  .

4. If the degrees of the numerator and denominator are equal, the limit is the ratio of their   coefficients.

5. What is the limit of f(x) = (3x^2 + 2x - 1) / (x^2 - 4x + 5) as x approaches infinity?

6. Evaluate the limit of g(x) = (x^3 - 5x) / (2x^4 + 7x^2 - 3) as x approaches infinity.

7. Determine the limit of h(x) = (4x^3 + 2x^2) / (x^2 - 6) as x approaches negative infinity.

8. Find the horizontal asymptote of the function f(x) = (5x - 3) / (2x + 1).

9. If the degree of the numerator is less than the degree of the denominator, the limit of a rational function as x approaches infinity is always 0.

10. The function y = sin(x) has a limit of 0 as x approaches infinity.