AP Calculus BC MC Practice (no calculator)

Front

What is the definition of a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some 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

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 derivative of a function?

Back

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.

Front

Explain the concept of an asymptote.

Back

An asymptote is a line that a graph approaches but never touches or crosses. There are vertical, horizontal, and oblique asymptotes.

Front

What is the difference between a definite and an indefinite integral?

Back

A definite integral computes the area under a curve between two points and results in a number, while an indefinite integral represents a family of functions and includes a constant of integration.

Front

What is L'Hôpital's Rule?

Back

L'Hôpital's Rule is a method for finding limits of indeterminate forms (0/0 or ∞/∞) by taking the derivative of the numerator and denominator.

Front

Define a critical point in calculus.

Back

A critical point of a function occurs where its derivative is zero or undefined, indicating potential local maxima or minima.

Front

What is the Mean Value Theorem?

Back

The Mean Value Theorem states that if a function is continuous on [a, b] and differentiable on (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Front

Explain the concept of concavity.

Back

Concavity refers to the direction of the curvature of a graph. A function is concave up if its second derivative is positive and concave down if its second derivative is negative.