AP Calculus AB Review

Front

What is the definition of velocity in calculus?

Back

Velocity is the rate of change of position with respect to time, often represented as the derivative of the position function, \( v(t) = \frac{dx}{dt} \).

Front

How do you find acceleration from a velocity function?

Back

Acceleration is the rate of change of velocity with respect to time, calculated as the derivative of the velocity function, \( a(t) = \frac{dv}{dt} \).

Front

What is the limit of a function as x approaches a value?

Back

The limit of a function as x approaches a value is the value that the function approaches as x gets arbitrarily close to that value.

Front

What does DNE stand for in calculus limits?

Back

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

Front

What is the limit of \( \frac{1}{x} \) as x approaches infinity?

Back

The limit of \( \frac{1}{x} \) as x approaches infinity is 0.

Front

What is the limit of a constant function as x approaches any value?

Back

The limit of a constant function as x approaches any value is the constant itself.

Front

What is the definition of a derivative?

Back

A derivative represents the instantaneous rate of change of a function with respect to its variable, defined as \( f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \).

Front

What is the relationship between the first and second derivatives?

Back

The first derivative of a function gives the slope of the tangent line (velocity), while the second derivative gives the rate of change of the first derivative (acceleration).

Front

How do you apply L'Hôpital's Rule?

Back

L'Hôpital's Rule is applied to evaluate limits of the form \( \frac{0}{0} \) or \( \frac{\infty}{\infty} \) by taking the derivative of the numerator and denominator.

Front

What is the Fundamental Theorem of Calculus?

Back

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