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Classical sequent calculus - Homepages of UvA/FNWI staff
Classical sequent calculus - Homepages of UvA/FNWI staff

AP Calculus AB Hands-On Activity: Rolle`s and Mean Value
AP Calculus AB Hands-On Activity: Rolle`s and Mean Value

Integration by inverse substitution
Integration by inverse substitution

Remarkable Theorem
Remarkable Theorem

... In a precalculus course, we gave the definition of ay if a > 0 and y is any rational number. But we did not define ay if y is irrational because this would have been an extremely difficult task without the use of calculus. We are now in a position where it is easy to define irrational exponents, and ...
CW 6 Solutions File
CW 6 Solutions File

A → (B → A)
A → (B → A)

... Assume V(B) = false; B came from Ei and Ei → B (which is Ej) If V(Ei) = true then V(Ej) = false and if V(Ei) = false then V(Ej) = true This means one of Ei and Ej is not an axiom or hypothesis This means that the false formula has to be the result of MP between Em and En which come before Ei (or Ej) ...
RT Section 4_5 L_Hopitals Rule
RT Section 4_5 L_Hopitals Rule

Average Value of a Function, The 2 nd Fundamental Theorem of
Average Value of a Function, The 2 nd Fundamental Theorem of

answers, in pdf - People @ EECS at UC Berkeley
answers, in pdf - People @ EECS at UC Berkeley

... Solution The length of the subintervals are ∆x = 1. Reading four values at the left end points, we get f (3) = 8, f (4) = 7, f (5) = 6, f (6) = 4. So the Riemann sum is ∆x[f (3) + f (4) + f (5) + f (6)] = 8 + 7 + 6 + 4 = 25 To draw approximating rectangles, sketch 4 rectangles with width 1; The firs ...
tan(x) - The Math Forum @ Drexel
tan(x) - The Math Forum @ Drexel

... a given arc length and its corresponding chord length, and in problems involving how deep a log of a certain specific gravity and a specific diameter sinks in water. ...
Solution - Math TAMU
Solution - Math TAMU

... asymptotes when x = ±1, and the x-axis is a horizontal asymptote when x → ±∞. In order for the graph to have negative slope everywhere on its domain and to have the origin as its only inflection point, the graph must look something like the following figure. ...
Final review
Final review

History Introduction
History Introduction

AP Calculus BC Saturday Study Session #1: The “Big” Theorems
AP Calculus BC Saturday Study Session #1: The “Big” Theorems

x dx
x dx

... If there no are secant factors and the power of the tangent is even and positive, convert a tangent-squared factor to a secant-squared factor. Then expand and ...
AP Calculus
AP Calculus

Math 131The Fundamental Theorem of Calculus (Part 2)
Math 131The Fundamental Theorem of Calculus (Part 2)

Microsoft Word Format
Microsoft Word Format

... Guidelines for Analyzing the Graph of a Function: 1. Find the x- and y-intercepts (set x and y to zero and solve for the other) 2. Find the vertical and horizontal asymptotes a. Vertical: set denominator equal to zero b. Horizontal: Lim f(x) = L (divide by highest power on denominator) x→ ∞ 3. Find ...
Math and Physics Refresher Geometry Calculus
Math and Physics Refresher Geometry Calculus

Lesson 18 – Finding Indefinite and Definite Integrals 1 Math 1314
Lesson 18 – Finding Indefinite and Definite Integrals 1 Math 1314

... Working with Riemann sums can be quite time consuming, and at best we get a good approximation. In an area problem, we want an exact area, not an approximation. The definite integral will give us the exact area, so we need to see how we can find this. We need to start by finding an antiderivative: A ...
dx - TaMATHawis!
dx - TaMATHawis!

... What you are finding: You are looking at problems in the form of " f (t) dt . This is asking for the rate dx a of change with respect to x of the accumulation function starting at some constant (which is irrelevant) and ending at that variable x. It is important to understand that this expression is ...
Summer Review Packet for Students Entering Calculus (all levels)
Summer Review Packet for Students Entering Calculus (all levels)

Calculus I Homework: Linear Approximation and Differentials Page
Calculus I Homework: Linear Approximation and Differentials Page

20 40 60 80 t 50 100 150 200
20 40 60 80 t 50 100 150 200

Calculus Maximus WS 2.1: Tangent Line Problem
Calculus Maximus WS 2.1: Tangent Line Problem

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History of calculus



Calculus, known in its early history as infinitesimal calculus, is a mathematical discipline focused on limits, functions, derivatives, integrals, and infinite series. Isaac Newton and Gottfried Leibniz independently invented calculus in the mid-17th century. However, each inventor claimed that the other one stole his work in a bitter dispute that continued until the end of their lives.
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