Limits at Infinity

Flashcards covering key concepts about limits at infinity in calculus.

Limit at Infinity

The value that a function approaches as the independent variable approaches infinity.

Horizontal Asymptote

A line y = L where at least one of the limits as x approaches infinity results in L.

Leading Term

The term of a polynomial with the highest exponent, which determines the limit as x approaches infinity.

Polynomial Limit Behavior

If f(x) is a polynomial, the limit as x approaches infinity is determined by the leading term.

Evaluation of Limits

The process of determining the limit of a function as the variable approaches a specific value.

Infinity in Limits

Indicates that the function value increases or decreases without bound as x approaches a certain direction.

If c is a real number, then lim of c as x approaches infinity

c.

If n is even, then lim of x^n as x approaches infinity

+∞.

If n is odd, then lim of x^n as x approaches infinity

+∞.

If n is odd and decreasing without bound, then lim of x^n as x approaches negative infinity

-∞.

Limit of a quotient

If lim f(x) = c and lim g(x) = ±∞, then lim f(x)/g(x) = 0.

Limit of a product

If lim f(x) = L₁ and lim g(x) = L₂, then lim [f(x)g(x)] = L₁L₂.