Calculus 1 Formula Sheet

Flashcards summarizing key calculus concepts, derivative rules, and integral formulas from the lecture notes.

Limit Laws

Rules that describe how limits can be computed with operations like addition and multiplication.

Continuity

A function f is continuous at a point a if lim_{x→a} f(x) = f(a).

Derivative of a constant

The derivative of a constant function is zero.

Power Rule

The derivative of x^n is n*x^(n-1).

Product Rule

The derivative of the product of two functions is f'g + fg'.

Quotient Rule

The derivative of a quotient of two functions is (f'g−fg')/g^2.

Trigonometric Derivatives

The derivatives of sine, cosine, tangent, and other trigonometric functions.

Inverse Trigonometric Derivative

The derivative of sin^{-1}x is 1/√(1-x^2).

Exponential Function Derivative

The derivative of e^x is e^x.

Antiderivative of x^n

The antiderivative ∫ x^n dx is x^(n+1)/(n+1) + C.

Addition of Definite Integrals

If you integrate from a to b, it's equal to F(b) - F(a).

Critical Points

Points where the derivative f'(x) is zero or undefined and are used to find local extrema.

Mean Value Theorem (MVT)

States that there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

Differential

In the context of calculus, dy = f'(x) dx.

Riemann Sum

An approximation of the integral of a function using finite sums.