Calculus Lecture Notes

These flashcards cover important concepts and definitions in Calculus based on the lecture notes.

Limit

The value a function approaches as x approaches a number.

Continuity

A function is continuous if the limit exists, the function exists, and they are equal.

Derivative

The instantaneous rate of change and slope of the tangent line.

Chain Rule

Take the derivative of the outside times the derivative of the inside.

Intermediate Value Theorem (IVT)

A continuous function takes all values between two points.

Mean Value Theorem (MVT)

There is a point where instantaneous rate equals average rate given the function is continuous on [a,b] and differentiable on (a,b).

Rolle’s Theorem

If endpoints are equal, there is a point where the derivative is zero.

Critical Point

Where the derivative is zero or undefined.

Concave Up

Second derivative is positive.

Inflection Point

Where concavity changes.

Integral

Accumulation, often the area under a curve.

Antiderivative

The reverse of a derivative.

Definite Integral

Net area between a function and the x-axis.

+C in Antiderivatives

Added because there are multiple antiderivatives.

Displacement

Net change in position.

Fundamental Theorem of Calculus (FTC)

Connects derivatives and integrals.

FTC Part 1

The derivative of an integral gives the function.

FTC Part 2

Evaluate integrals using F(b) − F(a).

f’(x)

Tells you the slope and whether the function is increasing or decreasing.

f’’(x)

Tells you the concavity.

Logs

Inverses of exponents.

Common Mistake with Limits

Not simplifying 0/0.

Common Mistake with Derivatives

Forgetting the chain rule.

Common Mistake with Integrals

Forgetting +C or misusing F(b) - F(a).