Limits at Infinity Worksheet
Explore the behavior of functions as x approaches infinity with this Grade 9 math worksheet on limits at infinity.
Includes
Standards
Topics
Limits at Infinity
Name:
Date:
Score:
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?
0
1
3
Infinity
6. Evaluate the limit of g(x) = (x^3 - 5x) / (2x^4 + 7x^2 - 3) as x approaches infinity.
0
1/2
2
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.
True
False
10. The function y = sin(x) has a limit of 0 as x approaches infinity.
True
False
Related Worksheets
Lagrange Error Bound Worksheet
This worksheet focuses on understanding and applying the Lagrange Error Bound to approximate functions using Taylor polynomials.
Derivative by Definition Worksheet
Practice problems for understanding and calculating derivatives using the limit definition.
Antidifferentiation Basics
This worksheet introduces fundamental concepts of antidifferentiation for Grade 9 students, focusing on finding antiderivatives of basic polynomial functions and understanding the constant of integration.
U-Substitution Practice Worksheet
Practice problems for U-substitution in calculus, covering basic definite and indefinite integrals.
Related Rates Worksheet
This worksheet focuses on related rates problems in Calculus, covering various geometric shapes and real-world scenarios.
Taylor Series Introduction
Explore the fundamentals of Taylor Series, including their definition, common expansions, and applications in approximating functions for Grade 9 Math.
Area Between Curves Worksheet
Calculate the area between two curves using integration.
Introduction to Differential Equations
This worksheet introduces fundamental concepts of differential equations, including order, linearity, and verification of solutions, suitable for Grade 9 math students.