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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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Differential Equations

Mixed approximation vs. full approximation for a power series expansion

6.8K threadsApr 17, 2026

Undergrad Mixed approximation vs. full approximation for a power series expansion

Apr 17, 2026

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Limits of m/n as x Approaches 1

spartas
Oct 21, 2015 · Replies 2 · Dec 6, 2015

Replies: 2

Word problem-population with logs

jibbs
Nov 16, 2015 · Replies 2 · Dec 6, 2015

Replies: 2

Undergrad Local max and min (including a domain)

King_Silver
Dec 4, 2015 · Replies 17 · Dec 6, 2015

Replies: 17

Graduate Which vectorial norm should I use?

RicardoMP
Dec 4, 2015 · Replies 2 · Dec 6, 2015

Replies: 2

Undergrad Integration Question: Confused on Limits of Integration

nmsurobert
Dec 3, 2015 · Replies 4 · Dec 5, 2015

Replies: 4

Differentiating tan2x: Steps & Solutions

Trix1
Dec 5, 2015 · Replies 2 · Dec 5, 2015

Replies: 2

Deriving f(x)=2x^x - Math Problem Solving

bguillenwork
Dec 5, 2015 · Replies 1 · Dec 5, 2015

Replies: 1

How to Simplify Derivatives Using Common Denominators

bugatti79
Dec 5, 2015 · Replies 1 · Dec 5, 2015

Replies: 1

High School Difference between Taylor Series and Taylor Polynomials?

NicolasPan
Dec 5, 2015 · Replies 4 · Dec 5, 2015

Replies: 4

Graduate Tangents to parametric equations

nomadreid
Dec 5, 2015 · Replies 2 · Dec 5, 2015

Replies: 2

Undergrad Fundamental Theorem of Calculus: Part One

in the rye
Dec 3, 2015 · Replies 12 · Dec 4, 2015

Replies: 12

Undergrad Is there a pattern between the sequence of cubes and the derivative of x^3?

jaja1990
Dec 4, 2015 · Replies 2 · Dec 4, 2015

Replies: 2

Graduate What is the closed form expression for the sum: Σx2/n! from 0 to N?

aaaa202
Dec 3, 2015 · Replies 1 · Dec 4, 2015

Replies: 1

Undergrad Initial Value Problem (complex example)

King_Silver
Dec 3, 2015 · Replies 10 · Dec 3, 2015

Replies: 10

How Is the Unit Normal Derived in an Epicycloid Equation?

bugatti79
Nov 17, 2015 · Replies 1 · Dec 2, 2015

Replies: 1

Undergrad Principal value of an integral

chiraganand
Dec 1, 2015 · Replies 10 · Dec 2, 2015

Replies: 10

Convergence Confusion

ognik
Nov 29, 2015 · Replies 6 · Dec 1, 2015

Replies: 6

Is the given function differentiable at the endpoints on the interval [0,5]?

karush
Dec 1, 2015 · Replies 4 · Dec 1, 2015

Replies: 4

How Do p^n Cos(nx) and p^n Sin(nx) Converge?

ognik
Dec 1, 2015 · Replies 2 · Dec 1, 2015

Replies: 2

Can Series Expansion Prove the Relation Between Inverse Coth and ln(x+1)/(x-1)?

ognik
Nov 28, 2015 · Replies 3 · Dec 1, 2015

Replies: 3

Undergrad Where can I start learning about Fourier Transforms/Series?

cmkluza
Nov 30, 2015 · Replies 13 · Dec 1, 2015

Replies: 13

Undergrad A question about some concepts from solving limits

xwolfhunter
Nov 5, 2015 · Replies 18 · Dec 1, 2015

Replies: 18

Undergrad Integration operation, and its relation to differentials

Mr Davis 97
Nov 30, 2015 · Replies 11 · Dec 1, 2015

Replies: 11

Finding \sum_{n=0}^{N-1} Cos (nx)

ognik
Nov 30, 2015 · Replies 3 · Dec 1, 2015

Replies: 3

Is the series $ \sum_{n=2}^{\infty} \frac{1}{n^2} $ converges?

ognik
Nov 26, 2015 · Replies 8 · Nov 30, 2015

Replies: 8

Undergrad Integral (area) of a revolved parabola

Karol
Nov 25, 2015 · Replies 8 · Nov 30, 2015

Replies: 8

Help with this calculus problem.

JWelford
Nov 30, 2015 · Replies 1 · Nov 30, 2015

Replies: 1

Interval of Convergence for Power Series

ineedhelpnow
Nov 29, 2015 · Replies 4 · Nov 30, 2015

Replies: 4

Graduate Finding a taylor series by substitution

Ibraheem
Nov 29, 2015 · Replies 1 · Nov 29, 2015

Replies: 1

Proving absolute values theorems

tmt1
Nov 29, 2015 · Replies 3 · Nov 29, 2015

Replies: 3

Undergrad Epsilon delta definition of limit

Avatrin
Nov 15, 2015 · Replies 20 · Nov 29, 2015

Replies: 20

Graduate Conformal and non-conformal transformations

JulieK
Nov 26, 2015 · Replies 1 · Nov 29, 2015

Replies: 1

Help With Integration Calculation - Struggling?

JWelford
Nov 29, 2015 · Replies 3 · Nov 29, 2015

Replies: 3

How Do You Estimate Sums Using the Euler-Mascheroni Constant?

ognik
Nov 28, 2015 · Replies 1 · Nov 29, 2015

Replies: 1

How do you calculate current in a circuit using integrals and limits?

Nemo1
Nov 26, 2015 · Replies 4 · Nov 29, 2015

Replies: 4

Graduate How is the inverse of a volume integral denoted?

dyn
Nov 28, 2015 · Replies 2 · Nov 28, 2015

Replies: 2

Graduate Is f(x,y,z) = 8xyz for Maximizing Volume in Ellipsoid?

mohamed el teir
Nov 28, 2015 · Replies 1 · Nov 28, 2015

Replies: 1

Undergrad How Does L'Hopital's Rule Apply to Lim (1/x)^tan(x) as x Approaches 0?

felipe oteiza
Nov 27, 2015 · Replies 12 · Nov 28, 2015

Replies: 12

Graduate This hypothesis is right about operators on convergent and divergent series?

MAGNIBORO
Nov 28, 2015 · Replies 4 · Nov 28, 2015

Replies: 4

Graduate Integrations involving hypergeometrics

CAF123
Nov 27, 2015 · Replies 2 · Nov 28, 2015

Replies: 2

Does the Series \(\sum_{n=1}^{\infty} \left[n(n+1)\right]^{-1/2}\) Converge?

ognik
Nov 26, 2015 · Replies 5 · Nov 27, 2015

Replies: 5

Induction Proof: Sum of Series $ \frac{1}{(2n-1)(2n+1)} = \frac{1}{2}$

ognik
Nov 26, 2015 · Replies 9 · Nov 27, 2015

Replies: 9

Graduate Fourier, square sign wave, f(x)sin(kx) integration

kostoglotov
Nov 27, 2015 · Replies 1 · Nov 27, 2015

Replies: 1

Undergrad Finding volume of a modified sphere using integrals

Parker Tibbs
Nov 26, 2015 · Replies 3 · Nov 26, 2015

Replies: 3

Find x Coordinate of Point A for Maths Integration Area Problem

MarkFL
Oct 23, 2013 · Replies 17 · Nov 26, 2015

Replies: 17

Graduate Understanding Convex Open Sets in Multivariable Calculus

geoffrey159
Nov 26, 2015 · Replies 11 · Nov 26, 2015

Replies: 11

High School Derivatives in Halliday's physics book?

kent davidge
Nov 25, 2015 · Replies 6 · Nov 25, 2015

Replies: 6

Undergrad What is the Antiderivative of 1/x in Calculus?

Cosmophile
Nov 4, 2015 · Replies 28 · Nov 25, 2015

Replies: 28

Undergrad Evaluating Total Error for Continuous Functions f and g

RaduAndrei
Nov 25, 2015 · Replies 6 · Nov 25, 2015

Replies: 6

Sum or difference formula (sin, cos, and tan)

Taryn1
Nov 24, 2015 · Replies 3 · Nov 24, 2015

Replies: 3

Graduate Integration by parts in spacetime

naima
Nov 9, 2015 · Replies 4 · Nov 24, 2015

Replies: 4

Undergrad Integration Help: Pls Explain Attached Picture

jderulo
Nov 19, 2015 · Replies 6 · Nov 24, 2015

Replies: 6

Undergrad How is a line integral over any closed surface 0?

transmini
Nov 23, 2015 · Replies 6 · Nov 23, 2015

Replies: 6

Undergrad How to evaluate this definite integral?

nashsth
Nov 22, 2015 · Replies 5 · Nov 22, 2015

Replies: 5

Undergrad Why can linear approximation equal quadratic approximation

JS-Student
Nov 21, 2015 · Replies 2 · Nov 22, 2015

Replies: 2

Convert Rectangular to Polar: Solving for $\theta$

karush
Nov 21, 2015 · Replies 5 · Nov 21, 2015

Replies: 5

Graduate Solve Tricky Integral in "Plane Waves Viewed from an Accelerated Frame

Jip
Jan 23, 2014 · Replies 1 · Nov 21, 2015

Replies: 1

Half wave symmetry and integrals

fernlund
Nov 21, 2015 · Replies 2 · Nov 21, 2015

Replies: 2

Graduate Calc of variations, minimizing functionals question

Coffee_
Nov 20, 2015 · Replies 5 · Nov 20, 2015

Replies: 5

Graduate Partial derivatives and chain rule?

mohamed el teir
Nov 20, 2015 · Replies 2 · Nov 20, 2015

Replies: 2

Yes, that makes sense! Thank you for explaining it to me.

bugatti79
Nov 14, 2015 · Replies 5 · Nov 20, 2015

Replies: 5

Undergrad Existence of Integral for (x^4 -x^6) / (x^2) from 0 to 4

Vsmith196
Nov 20, 2015 · Replies 7 · Nov 20, 2015

Replies: 7

Graduate Differentiating Integral with Green's function

RUber
Nov 19, 2015 · Replies 1 · Nov 20, 2015

Replies: 1

Undergrad How Is the Derivative of x=ρcosθ Computed?

DiracPool
Nov 18, 2015 · Replies 9 · Nov 20, 2015

Replies: 9

Graduate Deriving the Unit Normal for an Epicycloid: Understanding Equation 3.2.29

bugatti79
Nov 19, 2015 · Replies 2 · Nov 20, 2015

Replies: 2

Undergrad Find Lambda from this arbitrary triangle

bugatti79
Nov 18, 2015 · Replies 4 · Nov 19, 2015

Replies: 4

Is this the correct approach for using Taylor series in this problem?

Ironhorse1
Nov 19, 2015 · Replies 1 · Nov 19, 2015

Replies: 1

Graduate Riemann's proof of the existence of definite integrals

lingualatina
Nov 18, 2015 · Replies 1 · Nov 19, 2015

Replies: 1

Undergrad How to tell the difference in series

Kendall Pecere
Nov 18, 2015 · Replies 3 · Nov 18, 2015

Replies: 3

Graduate Proving equality of mixed second order partial derivatives

PWiz
Oct 18, 2015 · Replies 16 · Nov 18, 2015

Replies: 16

Undergrad Areas And Distances (Intro. to Definite Integral)

in the rye
Nov 17, 2015 · Replies 5 · Nov 17, 2015

Replies: 5

Undergrad What is the Higher Derivative of a function?

Nader AbdlGhani
Nov 15, 2015 · Replies 25 · Nov 17, 2015

Replies: 25

Undergrad Why can no one explain Power Series and Functions clearly

JoeTheKid
Nov 17, 2015 · Replies 2 · Nov 17, 2015

Replies: 2

Simple cylindrical coords problem

ognik
Nov 15, 2015 · Replies 3 · Nov 16, 2015

Replies: 3

Graduate Find infinitesimal displacement in any coordinate system

Msilva
Nov 15, 2015 · Replies 1 · Nov 15, 2015

Replies: 1

Undergrad How to find exact value of x/2=sinx?

greswd
Nov 10, 2015 · Replies 6 · Nov 15, 2015

Replies: 6

Graduate Stationary point for convex difference measure

noowutah
Nov 14, 2015 · Replies 1 · Nov 14, 2015

Replies: 1

Undergrad Infinite series with all negative terms

Ibraheem
Nov 14, 2015 · Replies 1 · Nov 14, 2015

Replies: 1

Graduate Strange integral of heaviside step function

cytochrome
Nov 14, 2015 · Replies 1 · Nov 14, 2015

Replies: 1

Solving Double Integrals: Order of Integration Explained

Estelle
Nov 13, 2015 · Replies 2 · Nov 13, 2015

Replies: 2

Graduate Conformal and non-conformal mappings

JulieK
Nov 11, 2015 · Replies 3 · Nov 12, 2015

Replies: 3

Undergrad What are the definitions and properties of Riemann sums?

Niaboc67
Nov 12, 2015 · Replies 2 · Nov 12, 2015

Replies: 2

Dc 8t14 product to sum indentity

karush
Nov 12, 2015 · Replies 5 · Nov 12, 2015

Replies: 5

Undergrad Equation of the tangent line in the direction of a vector

alex steve
Nov 12, 2015 · Replies 1 · Nov 12, 2015

Replies: 1

Undergrad Integrals: Fun to Solve Analytically!

LAZYANGEL
Nov 10, 2015 · Replies 1 · Nov 11, 2015

Replies: 1

Why Do Extra Terms Emerge in the Triple Vector Product with Del?

ognik
Nov 10, 2015 · Replies 5 · Nov 11, 2015

Replies: 5

Is the Cross Product of Orbital Angular Momentum Always Zero?

ognik
Nov 10, 2015 · Replies 4 · Nov 11, 2015

Replies: 4

Why Is There a Difference in Orbital Angular Momentum Calculation Methods?

ognik
Nov 10, 2015 · Replies 1 · Nov 11, 2015

Replies: 1

Undergrad How to get credit for a mathematics discovery?

Glype11
Nov 11, 2015 · Replies 3 · Nov 11, 2015

Replies: 3

Need Help finding Derivative (full explanation)

blakejohnston
Oct 7, 2015 · Replies 4 · Nov 11, 2015

Replies: 4

Graduate How is this a good approximation?

luxux
Nov 9, 2015 · Replies 12 · Nov 11, 2015

Replies: 12

Undergrad How to Calculate Velocity with Given Acceleration and Position Using Integration

Phys_Boi
Nov 10, 2015 · Replies 9 · Nov 10, 2015

Replies: 9

Solve Equation w/ Arcsin: How to Get 1/sqrt2 from pi/4

snowslider
Nov 10, 2015 · Replies 1 · Nov 10, 2015

Replies: 1

Gravity Gradient: Southward Displacement at $\phi = 30^{\circ}$

ognik
Nov 7, 2015 · Replies 10 · Nov 10, 2015

Replies: 10

Undergrad Calculus theorem/proof my teacher posted -- Not sure what it is....

Niaboc67
Nov 10, 2015 · Replies 2 · Nov 10, 2015

Replies: 2

Using Continuity to evaluate limit of a trig function

riri
Nov 9, 2015 · Replies 10 · Nov 9, 2015

Replies: 10

Undergrad Question regarding Newton's Method

King_Silver
Nov 7, 2015 · Replies 11 · Nov 9, 2015

Replies: 11

Undergrad Polygon sine functions? what is this?

Mathguy688
Nov 9, 2015 · Replies 1 · Nov 9, 2015

Replies: 1

Cant quite see this grad relation

ognik
Nov 7, 2015 · Replies 3 · Nov 9, 2015

Replies: 3

Undergrad Length of a line between origin and edge of a circle

jack476
Nov 8, 2015 · Replies 4 · Nov 8, 2015

Replies: 4

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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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