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Calculus I (Differential & intro Integral)

Free Calculus I (Differential & intro Integral) study guide: 8 units with summaries, key ideas, flashcards and 314 practice questions with step-by-step solutions.

Lines up with: AP Calculus AB; AP Calculus BC Units 1-8; CLEP Calculus.

Units

1. UNIT 01

   Limits & continuity

   A limit tells you the value f(x) heads toward as x gets close to a number, whether or not f actually equals that value there. Continuity is the case where the limit and the function value agree.
2. UNIT 02

   Definition of the derivative

   The derivative measures the instantaneous rate of change of a function, which is also the slope of its tangent line. It's defined as a limit of average rates of change.
3. UNIT 03

   Chain rule, implicit & inverse differentiation

   These rules let you differentiate functions built inside other functions, curves that aren't solved for y, and inverse functions.
4. UNIT 04

   Derivatives in context

   Derivatives describe real rates: how fast position, volume, cost or temperature is changing. This unit is about reading and using them in context.
5. UNIT 05

   Analytical applications of derivatives

   The first and second derivatives tell you the shape of a graph: where it rises and falls, where it bends, and where its highest and lowest points are.
6. UNIT 06

   Antiderivatives & the definite integral

   Integration adds up small pieces of change. The definite integral gives net signed area, and the Fundamental Theorem of Calculus connects it to antiderivatives.
7. UNIT 07

   Intro differential equations

   A differential equation relates a function to its own derivative. This unit covers solving the simplest kind and reading them as pictures.
8. UNIT 08

   Applications of integration

   Integrals turn rates into totals: distance from velocity, area between curves, volume of solids and the average value of a function.