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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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Graduate What is the arg() function in complex analysis?

Apr 5, 2005 · Replies 8 · Apr 6, 2005

Replies: 8

Views: 3K

Undergrad Can You Use Logarithmic Differentiation to Solve for a Base 2 Function?

Apr 6, 2005 · Replies 8 · Apr 6, 2005

Replies: 8

Views: 2K

Undergrad Limit as x approaches 2 from the right

Apr 6, 2005 · Replies 19 · Apr 6, 2005

Replies: 19

Views: 9K

Graduate Solve Convergence of Series Problem: Find Bounds for x_0

Apr 4, 2005 · Replies 7 · Apr 6, 2005

Replies: 7

Views: 2K

Undergrad Newton's Solution to Zeno's Paradox of the Arrow

Apr 4, 2005 · Replies 15 · Apr 6, 2005

Replies: 15

Views: 4K

Graduate Definitions of Measurable Functions

Apr 5, 2005 · Replies 9 · Apr 6, 2005

Replies: 9

Views: 4K

Undergrad Integration by parts (i think)

Mar 30, 2005 · Replies 2 · Apr 6, 2005

Replies: 2

Views: 3K

Undergrad Calculating Error in Algebraic Approximation: \Delta f(x,y)

Apr 5, 2005 · Replies 3 · Apr 5, 2005

Replies: 3

Views: 3K

Graduate Does R-omega satisfy the first countability axiom?

Mar 28, 2005 · Replies 2 · Apr 5, 2005

Replies: 2

Views: 5K

Graduate How Does the Strong Triangle Inequality Justify Equal p-adic Balls?

Apr 4, 2005 · Replies 4 · Apr 5, 2005

Replies: 4

Views: 2K

Graduate Lagrange multipliers and triangles

Apr 4, 2005 · Replies 2 · Apr 4, 2005

Replies: 2

Views: 9K

Undergrad Can I integrate this using only one integration by parts?

Apr 2, 2005 · Replies 1 · Apr 4, 2005

Replies: 1

Views: 2K

Graduate Can anyone solve integral with variable limits

Apr 1, 2005 · Replies 7 · Apr 4, 2005

Replies: 7

Views: 2K

Graduate Uniqueness of cubic interpolating polynomial

Apr 1, 2005 · Replies 4 · Apr 3, 2005

Replies: 4

Views: 5K

Undergrad What the heck does a line integral mean?

Apr 2, 2005 · Replies 5 · Apr 3, 2005

Replies: 5

Views: 14K

Graduate Calculating Volume of Cylinder with Double Integrals

Apr 3, 2005 · Replies 2 · Apr 3, 2005

Replies: 2

Views: 3K

Undergrad Optimizing Integration: Tips for Faster Calculations

Apr 2, 2005 · Replies 4 · Apr 3, 2005

Replies: 4

Views: 2K

Undergrad Finding Max/Min Points of f(x,y) in R^2

Apr 3, 2005 · Replies 2 · Apr 3, 2005

Replies: 2

Views: 2K

Undergrad Coulomb's Law & Gradient Function: Can Anyone Explain?

Mar 27, 2005 · Replies 2 · Apr 3, 2005

Replies: 2

Views: 6K

Undergrad Who else but pf could help me w/this prob.

Mar 4, 2005 · Replies 10 · Apr 2, 2005

Replies: 10

Views: 2K

Undergrad Indefinite Integral Help - Sin[x]Cos[x]Cos[x] & e^(Sqrt[x+1])

Apr 2, 2005 · Replies 5 · Apr 2, 2005

Replies: 5

Views: 2K

Graduate Is the Extremal Value Theorem Applicable to a Given Function on a Specific Area?

Apr 2, 2005 · Replies 7 · Apr 2, 2005

Replies: 7

Views: 3K

Graduate How to Derive the Cosine Power Series Using Euler's Identity?

Apr 1, 2005 · Replies 6 · Apr 2, 2005

Replies: 6

Views: 8K

Graduate Solve : 9 cosh9y dy = 4 sinh 4x dx

Apr 1, 2005 · Replies 3 · Apr 2, 2005

Replies: 3

Views: 3K

Graduate Help Me Prove Two Expressions Equal: Can You?

Apr 2, 2005 · Replies 5 · Apr 2, 2005

Replies: 5

Views: 2K

Undergrad What is the Integral of the Square Root of x^3 - 1?

Mar 21, 2005 · Replies 16 · Apr 2, 2005

Replies: 16

Views: 33K

Graduate Can This Differential Equation Solution Be Simplified Further?

Apr 1, 2005 · Replies 4 · Apr 2, 2005

Replies: 4

Views: 9K

Undergrad How can I integrate cos(3x)cos(2x) without using tables?

Apr 1, 2005 · Replies 7 · Apr 1, 2005

Replies: 7

Views: 5K

Graduate Minimize Heating and Cooling Costs w/ Partial Derivatives

Apr 1, 2005 · Replies 7 · Apr 1, 2005

Replies: 7

Views: 3K

Undergrad What is the Derivative of 1/(x√(x^2-1))?

Apr 1, 2005 · Replies 9 · Apr 1, 2005

Replies: 9

Views: 33K

Graduate Finding Fourier Series for u(x): Challenges with Integration

Apr 1, 2005 · Replies 2 · Apr 1, 2005

Replies: 2

Views: 2K

Undergrad Understanding Vector Division in Algebraic Structures

Apr 1, 2005 · Replies 12 · Apr 1, 2005

Replies: 12

Views: 37K

Undergrad Another convergence/divergence question

Mar 29, 2005 · Replies 17 · Apr 1, 2005

Replies: 17

Views: 3K

Undergrad Can you rephrase the question? What is e ?

Mar 31, 2005 · Replies 3 · Mar 31, 2005

Replies: 3

Views: 2K

High School Displacement Calculation: Speed x Time

Mar 31, 2005 · Replies 14 · Mar 31, 2005

Replies: 14

Views: 2K

Graduate Is the Cauchy-Hadamard Theorem Misrepresented on Mathworld?

Mar 31, 2005 · Replies 2 · Mar 31, 2005

Replies: 2

Views: 6K

Graduate Are there any other ways of parametizing S?

Mar 30, 2005 · Replies 7 · Mar 31, 2005

Replies: 7

Views: 3K

Undergrad Differential Calculus Problem Help w/ Complex Numbers

Mar 31, 2005 · Replies 2 · Mar 31, 2005

Replies: 2

Views: 2K

Graduate Integral equation with kernel K(st)

Mar 24, 2005 · Replies 2 · Mar 31, 2005

Replies: 2

Views: 3K

Graduate Why Are the Singular Points z=1/n Isolated in the Function f(z)=1/(sin(pi/z))?

Mar 30, 2005 · Replies 2 · Mar 31, 2005

Replies: 2

Views: 3K

Graduate How can you tell if a specific topological space is compact?

Mar 30, 2005 · Replies 5 · Mar 30, 2005

Replies: 5

Views: 2K

Graduate A function on a compact set is compact

Mar 28, 2005 · Replies 8 · Mar 30, 2005

Replies: 8

Views: 6K

Graduate What is the asymptotic behavior of S(n) with the Li(x) function?

Mar 28, 2005 · Replies 3 · Mar 30, 2005

Replies: 3

Views: 2K

Undergrad Simplifying a Limit with Factorization | Quick Help for Lim Questions

Mar 30, 2005 · Replies 9 · Mar 30, 2005

Replies: 9

Views: 2K

Undergrad Proving the Limit of (3n)^{\frac{1}{2n}} as n Goes to Infinity

Feb 26, 2005 · Replies 7 · Mar 29, 2005

Replies: 7

Views: 3K

Graduate Infinitie Series: Converge/Diverge question

Mar 28, 2005 · Replies 4 · Mar 29, 2005

Replies: 4

Views: 3K

Graduate Proving the Relationship Between Integrals and Root Pi Using Multiple Integrals

Mar 25, 2005 · Replies 9 · Mar 29, 2005

Replies: 9

Views: 10K

Undergrad Root of a complex number in cartesian

Mar 27, 2005 · Replies 15 · Mar 29, 2005

Replies: 15

Views: 8K

Undergrad Calculus III: Confused about Critical Points of f(x,y)?

Mar 28, 2005 · Replies 4 · Mar 29, 2005

Replies: 4

Views: 6K

Graduate Integrating $\frac{1}{\sqrt{2\beta x-\alpha x^2}}$

Mar 28, 2005 · Replies 11 · Mar 29, 2005

Replies: 11

Views: 3K

Undergrad Log n < O(n^ε) for Large n - Simple Function Growth

Mar 28, 2005 · Replies 9 · Mar 28, 2005

Replies: 9

Views: 2K

Undergrad How to Use LaGrange Multipliers to Find Highest and Lowest Points on an Ellipse?

Mar 21, 2005 · Replies 2 · Mar 28, 2005

Replies: 2

Views: 4K

Graduate Help with numerical integration

Mar 28, 2005 · Replies 10 · Mar 28, 2005

Replies: 10

Views: 3K

Undergrad Determining the Solution for d^2r/dt^2 = G*M/r^2 with Constant G and M

Mar 25, 2005 · Replies 18 · Mar 27, 2005

Replies: 18

Views: 3K

Graduate Does x->infiity (ln |cosx|)/x^2 exist?

Mar 25, 2005 · Replies 32 · Mar 27, 2005

2

Replies: 32

Views: 8K

Undergrad The integral of (sin 3t)^5 cos t dt

Mar 27, 2005 · Replies 12 · Mar 27, 2005

Replies: 12

Views: 3K

Graduate Where does the formula for dtheta in polar coordinates come from?

Mar 26, 2005 · Replies 3 · Mar 26, 2005

Replies: 3

Views: 2K

Graduate What is the solution to integrating \int\cos^{3/2}x \ dx?

Mar 25, 2005 · Replies 4 · Mar 26, 2005

Replies: 4

Views: 3K

Graduate Question about weak convergence in Hilbert space

Mar 18, 2005 · Replies 2 · Mar 26, 2005

Replies: 2

Views: 5K

Undergrad Calculus Boredom: Is It Common in Undergrad Math?

Mar 20, 2005 · Replies 40 · Mar 25, 2005

2

Replies: 40

Views: 13K

Undergrad Solving Telescoping Series with n Terms

Mar 18, 2005 · Replies 2 · Mar 25, 2005

Replies: 2

Views: 7K

Undergrad Help with 0.999...=1 Project - Urgent Assistance Needed

Mar 18, 2005 · Replies 2 · Mar 24, 2005

Replies: 2

Views: 2K

High School How Do You Verify This Trigonometric Identity?

Mar 24, 2005 · Replies 13 · Mar 24, 2005

Replies: 13

Views: 11K

Graduate Find Mass of Ball B w/ Triple Integrals & Cylindrical Coordinates

Mar 24, 2005 · Replies 5 · Mar 24, 2005

Replies: 5

Views: 8K

Undergrad Half vs Full Range Fourier Series: Odd & Even Functions

Mar 16, 2005 · Replies 2 · Mar 24, 2005

Replies: 2

Views: 2K

Graduate Is There a Numerical Method to Calculate the Minimum of a Functional?

Mar 16, 2005 · Replies 2 · Mar 23, 2005

Replies: 2

Views: 3K

Undergrad How do you deal with absolute values in your Integrals?

Mar 17, 2005 · Replies 2 · Mar 23, 2005

Replies: 2

Views: 5K

Undergrad Finding limits of integration during a change of variables

Mar 16, 2005 · Replies 2 · Mar 23, 2005

Replies: 2

Views: 8K

Graduate Is the Integral of (f(x)-q(g(x)))^2 Greater Than Zero?

Mar 22, 2005 · Replies 3 · Mar 23, 2005

Replies: 3

Views: 2K

Undergrad Area of Sphere Calc: Archimedes Method

Mar 15, 2005 · Replies 2 · Mar 22, 2005

Replies: 2

Views: 3K

Undergrad Is the Derivative of a Differentiable Function Always Continuous?

Mar 22, 2005 · Replies 2 · Mar 22, 2005

Replies: 2

Views: 2K

Graduate Proving Cauchy Sequence Subsequences

Mar 21, 2005 · Replies 12 · Mar 22, 2005

Replies: 12

Views: 2K

Graduate Find Min of f(x,y,z)=x^8+y^8+z^8 on x^4+y^4+z^4=4

Mar 15, 2005 · Replies 2 · Mar 22, 2005

Replies: 2

Views: 3K

Undergrad What is the Geometric Meaning of Grad f for Functions of Several Variables?

Mar 20, 2005 · Replies 5 · Mar 21, 2005

Replies: 5

Views: 3K

Undergrad How Do You Calculate the Average Value of a Function Between Two Points?

Mar 19, 2005 · Replies 6 · Mar 21, 2005

Replies: 6

Views: 3K

Graduate How Does the Riemann Sum Approximate the Limit of an Infinite Sum to Pi/4?

Mar 14, 2005 · Replies 2 · Mar 21, 2005

Replies: 2

Views: 7K

Undergrad Finding Concavity and Inflection Points of f(t) = 3cos^2(5t) on [-pi/5, pi/5]

Mar 13, 2005 · Replies 2 · Mar 21, 2005

Replies: 2

Views: 2K

Undergrad What's the Origin of This Integral Inequality?

Mar 20, 2005 · Replies 3 · Mar 20, 2005

Replies: 3

Views: 5K

Graduate How to Prove Log 2 Using Riemann Sums?

Mar 18, 2005 · Replies 10 · Mar 20, 2005

Replies: 10

Views: 6K

Undergrad Find the area bounded by y^2=x and y=x=2

Mar 18, 2005 · Replies 2 · Mar 20, 2005

Replies: 2

Views: 2K

Undergrad What Are the Real-Life Applications of Series and Sequences?

Mar 20, 2005 · Replies 2 · Mar 20, 2005

Replies: 2

Views: 2K

Graduate What are the solutions of w=tan z if w doesn't equal +i or -i?

Mar 18, 2005 · Replies 7 · Mar 19, 2005

Replies: 7

Views: 6K

Undergrad How to Calculate the Partial Derivative of a Function at the Origin?

Mar 12, 2005 · Replies 2 · Mar 19, 2005

Replies: 2

Views: 2K

Graduate Is the Definition for Fractional Derivative Correct?

Mar 12, 2005 · Replies 2 · Mar 19, 2005

Replies: 2

Views: 3K

Graduate Nonuniqueness of power series expansion

Mar 12, 2005 · Replies 2 · Mar 19, 2005

Replies: 2

Views: 3K

Undergrad Does the Equation x^2 = xsinx + cosx Have Exactly Two Real Roots?

Mar 7, 2005 · Replies 14 · Mar 18, 2005

Replies: 14

Views: 8K

Graduate Finding the Maximum Spread of Rumors Using Differential Equations

Mar 16, 2005 · Replies 9 · Mar 18, 2005

Replies: 9

Views: 3K

Undergrad Graphes: Increasing/Decreasing, Concave Up/Down, Inflection Points?

Mar 17, 2005 · Replies 7 · Mar 17, 2005

Replies: 7

Views: 14K

Graduate Why is del a Vector? Answers & Explanations

Mar 16, 2005 · Replies 24 · Mar 17, 2005

Replies: 24

Views: 8K

Graduate How to Find Surface Area of Intersecting Cylinders with Different Radii?

Mar 10, 2005 · Replies 2 · Mar 17, 2005

Replies: 2

Views: 3K

Undergrad Y=(x^2) +1 and y = - (x^2)? tangent

Mar 16, 2005 · Replies 2 · Mar 17, 2005

Replies: 2

Views: 3K

Undergrad Why Are These the Formulas for Derivatives and Logarithms?

Mar 16, 2005 · Replies 6 · Mar 17, 2005

Replies: 6

Views: 5K

Undergrad Integration by parts when a limit is infinity.

Mar 16, 2005 · Replies 14 · Mar 16, 2005

Replies: 14

Views: 15K

Graduate Why Doesn't the Second Derivative Work Starting with y^2-xy=2?

Mar 16, 2005 · Replies 5 · Mar 16, 2005

Replies: 5

Views: 3K

Graduate Can These Mathematical Proofs Determine the Limit of a Function?

Mar 8, 2005 · Replies 2 · Mar 16, 2005

Replies: 2

Views: 4K

Undergrad How Do Double Integrals and Polar Coordinates Relate to Symmetry Arguments?

Mar 15, 2005 · Replies 3 · Mar 16, 2005

Replies: 3

Views: 3K

Undergrad How do I Find the Derivative of sin(2x)?

Mar 15, 2005 · Replies 3 · Mar 15, 2005

Replies: 3

Views: 7K

Undergrad Irrational + irrational = rational

Mar 13, 2005 · Replies 38 · Mar 15, 2005

2

Replies: 38

Views: 39K

Graduate What are some vector calculus questions about gradient, divergence, and curl?

Mar 14, 2005 · Replies 9 · Mar 14, 2005

Replies: 9

Views: 3K

Undergrad General term of the sequence, if it exists

Mar 13, 2005 · Replies 9 · Mar 14, 2005

Replies: 9

Views: 6K

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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