Cumulative AP Calculus Flashcard

Front

Determine the limit of the function as x approaches infinity: f(x) = (3x^2 - 2)/(x^2 + 1)

Back

The limit is 3.

Front

What is the derivative of the position function?

Back

The derivative of the position function is the velocity function.

Front

Find the limit of the function as x approaches 2: f(x) = (x^2 - 4)/(x - 2)

Back

The limit is 4.

Front

What does DNE stand for in calculus?

Back

DNE stands for 'Does Not Exist', indicating that a limit does not approach a finite value.

Front

What is the Fundamental Theorem of Calculus?

Back

The Fundamental Theorem of Calculus links the concept of differentiation and integration, stating that if F is an antiderivative of f on an interval [a, b], then ∫_a^b f(x)dx = F(b) - F(a).

Front

What is the second derivative test used for?

Back

The second derivative test is used to determine the concavity of a function and to identify local maxima and minima.

Front

Define continuity at a point.

Back

A function f is continuous at a point c if: 1) f(c) is defined, 2) lim (x -> c) f(x) exists, and 3) lim (x -> c) f(x) = f(c).

Front

What is the limit of sin(x)/x as x approaches 0?

Back

The limit is 1.

Front

What is the relationship between acceleration and velocity?

Back

Acceleration is the derivative of velocity with respect to time.

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule is a method for finding limits of indeterminate forms by differentiating the numerator and denominator.