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Calculus Forum

Join experts in discussion of calculus topics. This may include topics on Elementary functions, Calculating limits, derivatives and integrals. Optimization problems and Homework help is available.

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Indefinite Integrals: How Were They Figured Out?

Jan 25, 2008 · Replies 3 · Jan 27, 2008

Replies: 3

Views: 4K

Integrating the Area Under a Shaded Region Using Substitution

Nov 26, 2007 · Replies 5 · Jan 27, 2008

Replies: 5

Views: 3K

Prevent Windshield Breakage: Minimizing Temperature Tolerance in mm

Jan 26, 2008 · Replies 1 · Jan 26, 2008

Replies: 1

Views: 3K

Complex Solutions to z^\alpha-1=0

Jan 22, 2008 · Replies 1 · Jan 26, 2008

Replies: 1

Views: 2K

Is it possible to define a bank angle for a helix roller-coaster track?

Jan 26, 2008 · Replies 1 · Jan 26, 2008

Replies: 1

Views: 2K

Integrals + Trig: Solve sin(2x)/23+cos(x)^2 dx

Jan 24, 2008 · Replies 9 · Jan 26, 2008

Replies: 9

Views: 3K

Proof Unbounded Sequence: Real Sequence |x_n|>1/n

Jan 23, 2008 · Replies 7 · Jan 26, 2008

Replies: 7

Views: 11K

Is there such a continuous function?

Jan 23, 2008 · Replies 8 · Jan 26, 2008

Replies: 8

Views: 3K

Proving the Derivative Rule for Rational Exponents

Jan 25, 2008 · Replies 7 · Jan 26, 2008

Replies: 7

Views: 6K

Mastering the Challenging Integral: Tips and Tricks for Solving x^(x-1)dx

Jan 23, 2008 · Replies 27 · Jan 25, 2008

Replies: 27

Views: 19K

Convexity and concavity of a function

Jan 23, 2008 · Replies 1 · Jan 25, 2008

Replies: 1

Views: 3K

Is (0,1) Uncountable If and Only If \Re is Uncountable?

Jan 24, 2008 · Replies 4 · Jan 24, 2008

Replies: 4

Views: 8K

Solution of 2 Equations with 3 Variables

Jan 24, 2008 · Replies 5 · Jan 24, 2008

Replies: 5

Views: 9K

What is the Natural Length of a Spring Based on Work Required for Stretching?

Jan 23, 2008 · Replies 2 · Jan 23, 2008

Replies: 2

Views: 15K

What is a single valued surface and why is it important in mathematics?

Jan 23, 2008 · Replies 4 · Jan 23, 2008

Replies: 4

Views: 2K

Definite Integral of x^2*sqrt(7x+9) from 0 to 1 - Need Help!

Jan 23, 2008 · Replies 4 · Jan 23, 2008

Replies: 4

Views: 3K

Surface Integral: Transform, Calculate and Add Up Results?

Jan 22, 2008 · Replies 4 · Jan 22, 2008

Replies: 4

Views: 5K

Can Gamma of negative integers be proven using a Laurent expansion?

Jan 21, 2008 · Replies 2 · Jan 22, 2008

Replies: 2

Views: 3K

Why does the first iterated integral exist but the second one does not?

Jan 1, 2008 · Replies 4 · Jan 21, 2008

Replies: 4

Views: 3K

How Do You Calculate f(3) for the Function f(x)?

Jan 21, 2008 · Replies 1 · Jan 21, 2008

Replies: 1

Views: 2K

Different between Partial and Ordinary derivative

Jan 21, 2008 · Replies 1 · Jan 21, 2008

Replies: 1

Views: 11K

Can you prove that two sequences with a specific feature have the same limit?

Jan 17, 2008 · Replies 9 · Jan 20, 2008

Replies: 9

Views: 3K

What is the Proof of the Euler Lagrange Equation?

Jan 19, 2008 · Replies 4 · Jan 20, 2008

Replies: 4

Views: 6K

Mastering Indefinite Integrals: Tips and Tricks for Evaluating Tricky Functions

Jan 18, 2008 · Replies 6 · Jan 18, 2008

Replies: 6

Views: 3K

How do I evaluate the integral [integral] x^2 cos mx dx using u-substitution?

Jan 18, 2008 · Replies 4 · Jan 18, 2008

Replies: 4

Views: 2K

Exponential Integral & Incomplete Gamma function

Jan 16, 2008 · Replies 2 · Jan 18, 2008

Replies: 2

Views: 7K

Minimization using first differential equation - help

Jan 17, 2008 · Replies 6 · Jan 18, 2008

Replies: 6

Views: 8K

Bread-Even Analysis: Solving for t

Jan 16, 2008 · Replies 3 · Jan 18, 2008

Replies: 3

Views: 7K

Limits at non-accumulation points

Jan 16, 2008 · Replies 3 · Jan 17, 2008

Replies: 3

Views: 4K

Where to Find Ebook Version of Thomas' Calculus (11th Edition)?

Jan 17, 2008 · Replies 2 · Jan 17, 2008

Replies: 2

Views: 7K

Solving the Integration Problem: Understanding arcos(x) = -arcsin(x)

Jan 15, 2008 · Replies 24 · Jan 17, 2008

Replies: 24

Views: 5K

Generalizations of the Inv. Function Thm.

Jan 11, 2008 · Replies 13 · Jan 17, 2008

Replies: 13

Views: 3K

Feynman integration trick - textbooks?

Dec 30, 2007 · Replies 13 · Jan 16, 2008

Replies: 13

Views: 23K

Integrate y = 2pi Int dz int(1-r^2)*r dr: Solution

Jan 15, 2008 · Replies 3 · Jan 15, 2008

Replies: 3

Views: 2K

Looking for a good problem book for PROOF-BASED integration

Dec 24, 2007 · Replies 3 · Jan 15, 2008

Replies: 3

Views: 4K

Another indefinite integral question?

Jan 13, 2008 · Replies 6 · Jan 15, 2008

Replies: 6

Views: 3K

Solving Inequalities: 4x² + 2x ≤ 3x + 2

Jan 14, 2008 · Replies 3 · Jan 14, 2008

Replies: 3

Views: 3K

Integral of a continuously differentiable function on [a,b].

Jan 13, 2008 · Replies 3 · Jan 14, 2008

Replies: 3

Views: 3K

Is Partial Fraction Decomposition Needed for This Integral?

Jan 13, 2008 · Replies 24 · Jan 14, 2008

Replies: 24

Views: 5K

Determine if a sequence {an} is monotonic, bounded, convergent

Jan 12, 2008 · Replies 3 · Jan 14, 2008

Replies: 3

Views: 4K

Need help: integration by substitution.

Jan 13, 2008 · Replies 1 · Jan 13, 2008

Replies: 1

Views: 2K

Volume of Frustum (Truncated Cone)

Jan 6, 2008 · Replies 5 · Jan 13, 2008

Replies: 5

Views: 23K

Navigating Maths: Finding Answers to Limit Questions

Dec 31, 2007 · Replies 33 · Jan 13, 2008

2

Replies: 33

Views: 5K

Integral Help: Solving -e^x/(e^x+1)

Jan 3, 2008 · Replies 13 · Jan 12, 2008

Replies: 13

Views: 3K

Open Source Math & Physics Software: Questions Answered

Jan 9, 2008 · Replies 1 · Jan 10, 2008

Replies: 1

Views: 3K

How to evaluate an indefinite integral

Dec 25, 2007 · Replies 14 · Jan 9, 2008

Replies: 14

Views: 4K

Why Does Sin(x) = 1 Have Different Solutions Compared to Sin(2x) = 1?

Jan 8, 2008 · Replies 2 · Jan 8, 2008

Replies: 2

Views: 4K

What is a Dyadic Form and What Does it Mean?

Jan 8, 2008 · Replies 2 · Jan 8, 2008

Replies: 2

Views: 6K

Solve Quadratic Question Urgently: Find Value of p

Jan 8, 2008 · Replies 4 · Jan 8, 2008

Replies: 4

Views: 2K

Convergent series - What is this N thing?

Jan 6, 2008 · Replies 7 · Jan 7, 2008

Replies: 7

Views: 3K

Taylor Polynomial Approximation

Jan 7, 2008 · Replies 1 · Jan 7, 2008

Replies: 1

Views: 4K

Looking for Calculus Text or Ebook? Help a Student in Need!

Jan 5, 2008 · Replies 2 · Jan 6, 2008

Replies: 2

Views: 4K

I'm practicing how to differentiate equations.

Jan 5, 2008 · Replies 5 · Jan 6, 2008

Replies: 5

Views: 3K

Calculus Books for Beginners: Recommendations

Jan 4, 2008 · Replies 16 · Jan 4, 2008

Replies: 16

Views: 6K

Cauchy Condensation Proof

Jan 2, 2008 · Replies 6 · Jan 4, 2008

Replies: 6

Views: 6K

Understanding f(x) and y in the function f(x) = x² + 4: Explained

Jan 3, 2008 · Replies 2 · Jan 4, 2008

Replies: 2

Views: 2K

How Can I Evaluate This Integral of a Rational Function?

Jan 2, 2008 · Replies 6 · Jan 3, 2008

Replies: 6

Views: 4K

How Do You Find the X-Coordinate of Point Q on Curve C?

Jan 2, 2008 · Replies 3 · Jan 3, 2008

Replies: 3

Views: 3K

Mastering Integration by Parts: Proving the Indefinite Integral Formula

Jan 1, 2008 · Replies 2 · Jan 1, 2008

Replies: 2

Views: 4K

Maximizing Scalar Increase: Understanding the Direction of the Gradient

Jan 1, 2008 · Replies 4 · Jan 1, 2008

Replies: 4

Views: 12K

How Do You Prove the Summation Formula S_{n} = \frac{n}{2}(2a + L)?

Jan 1, 2008 · Replies 1 · Jan 1, 2008

Replies: 1

Views: 6K

Finding this set of values for x

Jan 1, 2008 · Replies 1 · Jan 1, 2008

Replies: 1

Views: 6K

Understanding Limits & Minimum in Spivak's Calculus

Dec 31, 2007 · Replies 2 · Jan 1, 2008

Replies: 2

Views: 3K

Finding One-Sided Limits: The Simplest Way

Jan 1, 2008 · Replies 4 · Jan 1, 2008

Replies: 4

Views: 11K

High School Calculus: Differentiation vs. Integration

Dec 1, 2007 · Replies 22 · Jan 1, 2008

Replies: 22

Views: 16K

Book Wrong? Solving g'(x) = [p(2r sin rx + n)^(p-1)] * (2r^2cos rx)

Dec 31, 2007 · Replies 3 · Dec 31, 2007

Replies: 3

Views: 5K

Does y = ax^3 + bx^2 + cx + d Have Two Distinct Turning Points if b^2 > 3ac?

Dec 30, 2007 · Replies 5 · Dec 30, 2007

Replies: 5

Views: 4K

Partial Fractions: Solve Integral of 1/y^2-1 dx

Dec 30, 2007 · Replies 5 · Dec 30, 2007

Replies: 5

Views: 5K

Solving differential equations with definite integrals?

Dec 28, 2007 · Replies 2 · Dec 30, 2007

Replies: 2

Views: 14K

Can Complex Analytic Functions Have Uncountable Singular Points?

Dec 30, 2007 · Replies 3 · Dec 30, 2007

Replies: 3

Views: 4K

Is the Integral Syntax Correct for dx = v dt and x = \int v dt?

Dec 29, 2007 · Replies 5 · Dec 30, 2007

Replies: 5

Views: 3K

Why Straight Lines? Uncovering the Theory Behind f(x,y)=0

Dec 30, 2007 · Replies 3 · Dec 30, 2007

Replies: 3

Views: 3K

Integrating (x^2+1)^{-3/2} using Substitution

Dec 26, 2007 · Replies 14 · Dec 29, 2007

Replies: 14

Views: 4K

Differentiation operators similar to exponents?

Dec 26, 2007 · Replies 17 · Dec 29, 2007

Replies: 17

Views: 5K

Difference between d²y/d²x and d²y/dx²

Dec 27, 2007 · Replies 9 · Dec 28, 2007

Replies: 9

Views: 11K

The contiunity equation and differentiation

Dec 25, 2007 · Replies 23 · Dec 28, 2007

Replies: 23

Views: 4K

Solve the Limit on a_n of Log^n and Pi^n(3)

Dec 20, 2007 · Replies 29 · Dec 28, 2007

Replies: 29

Views: 6K

Constructing a Borel set with desired properties

Dec 16, 2007 · Replies 7 · Dec 27, 2007

Replies: 7

Views: 3K

Proving Integration Notation for Smooth Function f

Dec 25, 2007 · Replies 5 · Dec 26, 2007

Replies: 5

Views: 3K

How to Evaluate Indefinite Integrals with Radical Expressions?

Dec 25, 2007 · Replies 6 · Dec 25, 2007

Replies: 6

Views: 4K

A tricky countour integral (branch cuts)

Dec 25, 2007 · Replies 1 · Dec 25, 2007

Replies: 1

Views: 5K

Trig Differentiation Memorization help

Dec 22, 2007 · Replies 15 · Dec 25, 2007

Replies: 15

Views: 6K

What's the Best Way to Evaluate This Limit?

Dec 24, 2007 · Replies 3 · Dec 24, 2007

Replies: 3

Views: 3K

Evaluating Undefined Limit of Calculus Final

Dec 23, 2007 · Replies 6 · Dec 23, 2007

Replies: 6

Views: 12K

Solve the Integration by Parts Equation: xlnx dx | Senior in AP Calculus BC

Dec 20, 2007 · Replies 3 · Dec 23, 2007

Replies: 3

Views: 2K

What is the significance of the number e and Euler's formula?

Dec 9, 2007 · Replies 37 · Dec 22, 2007

2

Replies: 37

Views: 8K

Weak Convergence of A in l^2: Does it Preserve Closedness?

Sep 23, 2007 · Replies 1 · Dec 21, 2007

Replies: 1

Views: 3K

How Can dx and dy Be Manipulated in Differential Equations and Integrals?

Dec 7, 2007 · Replies 23 · Dec 20, 2007

Replies: 23

Views: 8K

Algebraic Simplification of 3^{x^2-x-z}+3^{y^2-y-x}+3^{z^2-z-y}=1

Dec 18, 2007 · Replies 2 · Dec 19, 2007

Replies: 2

Views: 1K

Hints for Integrating sqrt(1 +a^2*x^2)dx

Dec 19, 2007 · Replies 2 · Dec 19, 2007

Replies: 2

Views: 2K

What Are Conformal Maps in Complex Analysis?

Dec 18, 2007 · Replies 1 · Dec 19, 2007

Replies: 1

Views: 2K

Something a little odd - Lebesgue vs Riemann integral

Dec 18, 2007 · Replies 6 · Dec 19, 2007

Replies: 6

Views: 7K

Why can i not use induction here?

Dec 17, 2007 · Replies 3 · Dec 18, 2007

Replies: 3

Views: 3K

Calculus I - without a calculator

Dec 17, 2007 · Replies 8 · Dec 18, 2007

Replies: 8

Views: 22K

Spivak, Calculus - Where to find or is it covered?

Dec 11, 2007 · Replies 4 · Dec 18, 2007

Replies: 4

Views: 4K

Dy/dx as Fraction: A-Level Maths/Further Maths Explanation

Dec 15, 2007 · Replies 5 · Dec 17, 2007

Replies: 5

Views: 11K

Is there solution for this kind of equation

Dec 17, 2007 · Replies 2 · Dec 17, 2007

Replies: 2

Views: 3K

Understanding the Exponential Property of Complex Numbers

Dec 17, 2007 · Replies 2 · Dec 17, 2007

Replies: 2

Views: 3K

Which AP Calculus Exam Should I Take? AB or BC

Dec 14, 2007 · Replies 21 · Dec 17, 2007

Replies: 21

Views: 5K

How do I specify derivatives in C++ for use in the 4th order Runge-Kutta method?

Dec 16, 2007 · Replies 1 · Dec 17, 2007

Replies: 1

Views: 2K

Calculus

Welcome to the Calculus forum!

Calculus is a branch of mathematics that focuses on the study of continuous change and motion.

It comprises two primary branches: differential calculus, which examines rates of change and slopes of curves, and integral calculus, which deals with accumulation and the calculation of areas under curves. Developed independently by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, calculus has become a fundamental tool in various scientific and engineering disciplines.

It provides a powerful framework for analyzing and modeling dynamic processes, such as motion, growth, and decay, and forms the basis for understanding concepts like derivatives and integrals, essential for advanced mathematical and scientific studies.

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