AP Calculus Midterm Review

Front

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

Back

The limit of a function as x approaches a certain value is the value that the function approaches as x gets closer to that value.

Front

Find the limit: lim (x -> 1) (x^2 - 1)/(x - 1)

Back

The limit is 2.

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 derivative of sin(x)?

Back

The derivative of sin(x) is cos(x).

Front

What is the derivative of cos(x)?

Back

The derivative of cos(x) is -sin(x).

Front

What is the derivative of tan(x)?

Back

The derivative of tan(x) is sec^2(x).

Front

What is the slope of the tangent line to a curve at a point?

Back

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

Front

Find the limit as x approaches 0: lim (x -> 0) (sin(x)/x)

Back

The limit is 1.

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 limit of a constant function?

Back

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