Limit Definition
The Power Rule
Calculus & Limits: The Key Masterlist 🧠
The value a function approaches as the input gets closer to a specific number.
The rate of change or the slope (gradient) of a function at any given point.
The reverse of a derivative. Used to find the area under a curve.
A concept describing something without any bound or end. Crucial for limits.
Represents a small change in the value of x.
The mathematical relationship where each input has exactly one output.
Added to indefinite integrals to represent any possible constant value.
A common way to write the first derivative of a function.
A function with no holes, jumps, or vertical asymptotes in its graph.
A straight line that just touches a curve at a single point.
An ordered list of numbers, often used to study convergence in limits.
The symbol for summation, used in Riemann sums to find integrals.
An infinitesimal change in the dependent variable y.
Method to find the derivative of a composite function f(g(x)).
When a sequence or function approaches a specific finite value.
The steepness of a line, found using the derivative in calculus.
The Calculus War: A Legacy ⚔️
ISAAC NEWTON (1660s)
He called it the "Method of Oations." Newton developed calculus to explain why planets move in ellipses. He kept his work secret for years, using it only to solve physics problems.
GOTTFRIED LEIBNIZ (1670s)
Independently discovered calculus in Germany. He gave us the notation we use today, like the integral sign (∫) and dy/dx. His version was much easier for other mathematicians to use.
THE GREAT CONTROVERSY
For decades, they argued over who stole from whom! Today, historians agree they both discovered it independently. Newton is the father of its application, but Leibniz is the father of its language.