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.

Threads

Is 1/(1+sinx) + 1/(1-sinx) Equal to 2sec2x?

  • chlobuggy
  • · Replies 2 ·
Replies
2

Graduate Cauchy Riemann conditions/equation

  • MartinV05
  • · Replies 2 ·
Replies
2

Why does sin(x) end up in the denominator when differentiating ln(sin(x))?

  • DeusAbscondus
  • · Replies 6 ·
Replies
6

How is the constant '4' handled in differentiation of $y=4\cos(x^3-2x)$?

  • DeusAbscondus
  • · Replies 9 ·
Replies
9

Undergrad Why is the Height of Each Cylinder in a Cone dS and not dH?

  • dtseng96
  • · Replies 5 ·
Replies
5

Undergrad Algorithms for infinite geometric series via long division?

  • AdkinsJr
  • · Replies 2 ·
Replies
2

Undergrad When plotting graphs in polar coordinates, how does one know when to

  • hale2bopp
  • · Replies 1 ·
Replies
1

Undergrad Does the fundamental theorem of calculus require the integrand to be independent of x?

  • c.teixeira
  • · Replies 6 ·
Replies
6

Graduate Why does the sinc function approach zero as the argument approaches infinity?

  • McLaren Rulez
  • · Replies 4 ·
Replies
4

Graduate No Limit Points in Natural Numbers: Problem with Proof?

  • Dschumanji
  • · Replies 3 ·
Replies
3

Graduate Fourier Transform and Limit of Euler's Formula

  • gordon831
  • · Replies 2 ·
Replies
2

Undergrad What is the ε-δ definition of continuity of f(x) at x=0?

  • Joydeep B
  • · Replies 1 ·
Replies
1

Undergrad Why does d/dx (dy/dx)² give 2(d²y/dx²) and not 2(dy/dx)(d²y/dx²)?

  • Mgarrettny
  • · Replies 4 ·
Replies
4

Undergrad Why does ∫3/√(x²-4) give different answers?

  • Cetullah
  • · Replies 3 ·
Replies
3

Graduate Integral want same answer as book

  • Steve Drake
  • · Replies 6 ·
Replies
6

Graduate How to obtain a 2D-coordinate system from two family of curves?

  • mnb96
  • · Replies 4 ·
Replies
4

Graduate What Is the Mathematical Substitution Used in This Integral Notation?

  • Alesak
  • · Replies 1 ·
Replies
1

Undergrad Proof that the area under the curve dh/dt against t = height

  • expatiated
  • · Replies 1 ·
Replies
1

Undergrad Making Sense of the Chain Rule: Can I Multiply to Find dy/dx?

  • Bashyboy
  • · Replies 3 ·
Replies
3

Undergrad How Can You Solve the Infinite Series \(\sum_{n=1}^{\infty}\frac{n}{k^{n}}\)?

  • YvesSch
  • · Replies 2 ·
Replies
2

Graduate Partial Derivatives with Respect To Lines That Are Not In The Direction of Axis

  • Byron Chen
  • · Replies 3 ·
Replies
3

Graduate Representing real functions as improper integrals with ω(t,x)

  • Sigma057
  • · Replies 8 ·
Replies
8

Integrating $\frac{1}{x^r-1}$ with r>1

  • bincy
  • · Replies 5 ·
Replies
5

High School What Does Δy/Δx Represent in Basic Differentiation?

  • raeshun
  • · Replies 4 ·
Replies
4

Undergrad Deriving the volume and surface area of a cone

  • dtseng96
  • · Replies 7 ·
Replies
7

High School How can I find the roots of a polynomial like x^3-7x+6?

  • Cetullah
  • · Replies 7 ·
Replies
7

Undergrad Are All Integrals Solvable by Changing Coordinate Systems?

  • hover
  • · Replies 3 ·
Replies
3

Graduate How Are Square Roots Defined for Complex Numbers?

  • Bacle2
  • · Replies 21 ·
Replies
21

Undergrad Two-Path Test: Understanding Variable Function Limits

  • assed
  • · Replies 3 ·
Replies
3

Undergrad Where is the error in this calculation that gives 1+2+4+8+16+...=-1?

  • Routaran
  • · Replies 14 ·
Replies
14

Limit of Function w/ 0<q<1: Solved by Bincy

  • bincy
  • · Replies 2 ·
Replies
2

Undergrad Integral test and ratio test on haromonic series.

  • avman
  • · Replies 1 ·
Replies
1

Graduate I'm having trouble with an integral for my QM senior thesis

  • jmm5872
  • · Replies 9 ·
Replies
9

Finding the Metric Tensor for a Flat 2D Plane with Rotated Coordinates

  • andrey21
  • · Replies 13 ·
Replies
13

Graduate How did Madhava come up with the Arctan series?

  • imurme8
  • · Replies 4 ·
Replies
4

Graduate Second derivative relationships of substituted varaibles

  • PhilDSP
  • · Replies 6 ·
Replies
6

Simple limit question in attached pdf

  • DeusAbscondus
  • · Replies 15 ·
Replies
15

Undergrad Help Understanding Stewart Chain Rule Proof [Picture Provided]

  • nickadams
  • · Replies 6 ·
Replies
6

Undergrad Is there a way to prove that A(x) is minimum when x=2r?

  • Rush123
  • · Replies 2 ·
Replies
2

Undergrad Use of a derivative or a gradient to minimize a function

  • onako
  • · Replies 3 ·
Replies
3

Is the Derivative of f(x)=1/x^3 Correctly Calculated as -3/x^4?

  • DeusAbscondus
  • · Replies 2 ·
Replies
2

Undergrad What Does the Lower Limit in This Integral Represent?

  • femiadeyemi
  • · Replies 4 ·
Replies
4

Undergrad Minimizing Sum of Absolute Values

  • adoado
  • · Replies 33 ·
2
Replies
33

Undergrad Need a function with a jump discontinuity

  • mesa
  • · Replies 19 ·
Replies
19

Undergrad Understanding Series Convergence

  • BarringtonT
  • · Replies 5 ·
Replies
5

Undergrad Approximation of a function in limit of small and large x

  • FrankDrebon
  • · Replies 4 ·
Replies
4

Undergrad Why convert a function into a power series

  • BarringtonT
  • · Replies 4 ·
Replies
4

Undergrad Rate at which things appear smaller and establishing a baseline

  • LykosPF4
  • · Replies 3 ·
Replies
3

Graduate Shortest path to the Calculus of Variations

  • GoutamTmv
  • · Replies 5 ·
Replies
5

Find Volume of Wine Glass on Side with Solids of Revolution

  • Jipsonburger
  • · Replies 4 ·
Replies
4

Graduate How to compute the area of a hyperboloid of revolution?

  • DaviesX
  • · Replies 2 ·
Replies
2

Undergrad Initial velocity for 900-foot projectile launch and restaurant wait time percentile

  • andrija
  • · Replies 1 ·
Replies
1

Undergrad Does this Divergence Test problem converge?

  • flyintiger
  • · Replies 4 ·
Replies
4

Undergrad How to calculate the derivative of ln(x) using the limit

  • Cristopher
  • · Replies 11 ·
Replies
11

Graduate Wikipedia error about the complementary error function?

  • AxiomOfChoice
  • · Replies 3 ·
Replies
3

Undergrad Not Understanding Derivative Notation

  • Gibby_Canes
  • · Replies 2 ·
Replies
2

Graduate Difference between small delta t, big delta t, and dt?

  • schrodingerscat11
  • · Replies 3 ·
Replies
3

Undergrad Chain rule with linear compositions f(x) = abx

  • V0ODO0CH1LD
  • · Replies 7 ·
Replies
7

Graduate Integration techniques and Cauchy prinicpal value

  • Stephen Tashi
  • · Replies 2 ·
Replies
2

Undergrad Why does dx/dy differ from dy/dx for inverse functions?

  • Scintillation
  • · Replies 1 ·
Replies
1

Number of Molecules vs Velocity: Finding N for v > v_0

  • alexmahone
  • · Replies 12 ·
Replies
12

Graduate Choosing constants to make integral convergent

  • sr3056
  • · Replies 5 ·
Replies
5

Undergrad Why does L'Hôpital's rule give different limits for the same function?

  • krackers
  • · Replies 4 ·
Replies
4

Undergrad Proof for first principle equation in derivatives?

  • Swetasuria
  • · Replies 8 ·
Replies
8

Undergrad How Is the Operator d/dx Conceptualized in Calculus?

  • FlyingPanda
  • · Replies 4 ·
Replies
4

Finding sin(α)+cos(β) given cos(α)+cos(β)−cos(α+β)=3/2

  • DrunkenOldFool
  • · Replies 5 ·
Replies
5

How Do You Integrate 1/(x^2 + 1)^2 Using the Hermite-Ostrogradski Method?

  • righteous818
  • · Replies 2 ·
Replies
2

Graduate Generating Functions for n+1 Integer Set: Closed Form

  • anthony2005
  • · Replies 1 ·
Replies
1

Undergrad Why do derivatives and integrals cancel each other?

  • krackers
  • · Replies 10 ·
Replies
10

Graduate Differentiation of the l1 norm of gradient

  • wilsonnl
  • · Replies 2 ·
Replies
2

Graduate Lebesgue Measurable but not Borel sets.

  • Bacle2
  • · Replies 3 ·
Replies
3

Graduate Deducing Maclaurin series converges from Leibniz formula

  • sr3056
  • · Replies 3 ·
Replies
3

Undergrad How do you find the slope of a line in 3D coordinate system given two points?

  • Lizwi
  • · Replies 3 ·
Replies
3

Graduate Proving inequality bounds for (1-1/n)^n using logarithmic inequalities

  • sr3056
  • · Replies 6 ·
Replies
6

Undergrad How can I find the Proper starting point in FindRoot command?

  • Mona_r
  • · Replies 7 ·
Replies
7

Graduate Find the function for this Taylor series

  • arithmetic
  • · Replies 14 ·
Replies
14

Graduate Find F(2,4) of Differentiable Function

  • antjm
  • · Replies 6 ·
Replies
6

Undergrad Why can't you break the limit of x*sin(1/x) into two separate limits?

  • krackers
  • · Replies 12 ·
Replies
12

Graduate Applying the FTC to an arbitrary solution of the Schrodinger equation

  • AxiomOfChoice
  • · Replies 2 ·
Replies
2
Replies
3

Undergrad Calculate throw angle to have the curve cross a certain point

  • kiriri
  • · Replies 8 ·
Replies
8

Graduate Chain rule with multiple variables

  • Undoubtedly0
  • · Replies 6 ·
Replies
6

Undergrad Anyone remember how to solve 0^0?

  • kings_gambit
  • · Replies 2 ·
Replies
2

Undergrad When can a limit exist at a discontinuity?

  • Stu21
  • · Replies 1 ·
Replies
1

Integral from negative infinity to infinity

  • juantheron
  • · Replies 1 ·
Replies
1

Graduate Why Doesn't Stoke's Theorem Require a Simply Connected Manifold?

  • Trifis
  • · Replies 19 ·
Replies
19

Graduate Proving Global Max/Min for Function w/ 2 Variables: Advice Needed

  • porroadventum
  • · Replies 5 ·
Replies
5

Graduate Whittaker and Watson examples solutions / hints

  • TriggerFish
  • · Replies 3 ·
Replies
3

Graduate Integral from Unsolvable Equation

  • TheFool
  • · Replies 40 ·
2
Replies
40

Graduate Differential Squared: Do We Always Assume (dx)^2=0?

  • learner928
  • · Replies 3 ·
Replies
3

Undergrad How does the proof of L'Hopital's rule show that the limit is equal to A?

  • modnarandom
  • · Replies 1 ·
Replies
1

Undergrad Evaluating limit as h->0 of (e^h-1)/h

  • autodidude
  • · Replies 8 ·
Replies
8

Graduate Indefinite Integral for -.5*(ln(2))^2

  • SumThePrimes
  • · Replies 3 ·
Replies
3

Graduate How Does the Tanh(x) Approximation Relate to Small Angles?

  • wil3
  • · Replies 6 ·
Replies
6

Graduate What is the Ricci tensor and what does it represent mathematically?

  • mathsTKK
  • · Replies 1 ·
Replies
1

Undergrad Why does lim(h→0)(a^h−1)/h not equal 0/0?

  • Bashyboy
  • · Replies 6 ·
Replies
6

Graduate Integral with Cauchy Prinicpal value

  • M.B.
  • · Replies 6 ·
Replies
6

Graduate Integral? Average Velocity of a Spinning Propeller

  • jaguar7
  • · Replies 7 ·
Replies
7

Graduate Problem with Integrating by parts

  • aries0152
  • · Replies 3 ·
Replies
3

Undergrad Multivariable Calculus, Partial Derivatives and Vectors

  • V0ODO0CH1LD
  • · Replies 1 ·
Replies
1