Examples for

Calculus & Analysis

Calculus is the branch of mathematics studying the rate of change of quantities and the length, area and volume of objects. With the ability to answer questions from single and multivariable calculus, Wolfram|Alpha is a great tool for computing limits, derivatives and integrals and their applications, including tangent lines, extrema, arc length and much more.

Integrals

Compute definite and indefinite integrals of functions. Integrate with respect to one or more variables.

Compute an indefinite integral:

Compute a definite integral:

Compute an improper integral:

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Limits

Explore the limit behavior of a function as it approaches a single point or asymptotically approaches infinity.

Compute a limit:

Compute a one-sided limit:

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Products

Compute an indexed product by multiplying a finite or infinite number of terms.

Compute an indexed product:

Compute an infinite product:

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Vector Analysis

Apply the curl, the gradient and other differential operators to scalar and vector fields.

Compute the gradient of a function:

Calculate alternate forms of a vector analysis expression:

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Continuity

Find discontinuities and continuous intervals of a function. Also determine whether particular discontinuities are removable or infinite due to an asymptote.

Determine whether a function is continuous:

Locate discontinuities of a function:

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Derivatives

Take the derivative of single or multivariate functions. Compute the partial derivative of expressions with more than one variable.

Calculate the derivative of a function:

Compute higher derivatives:

Compute partial derivatives:

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Sequences

Calculate and examine sequences of integers or other numerical values. Find continuations and formulas for known or unknown sequences.

Analyze a sequence:

Compute a possible formula and continuation for a sequence:

Solve a recurrence:

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Series Expansions

Find Taylor series, Laurent series and more about any point.

Find a Taylor series expansion:

Specify the center point and the order of the expansion:

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Integral Transforms

Calculate the Fourier transform, Laplace transform and other integral transforms of functions.

Compute a Fourier transform:

Compute a Laplace transform:

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GO FURTHER

Step-by-Step Solutions for Calculus

Calculus Web App

Free Unlimited Calculus Practice Problems

RELATED EXAMPLES

  • Algebra
  • Complex Analysis
  • Coordinate Geometry
  • Differential Equations
  • Numerical Analysis
  • RELATED WOLFRAM RESOURCES

  • Wolfram Community Calculus Group
  • Sums

    Compute the value of indexed summations, or sums of sequences of values. Compute infinite sums and find convergence conditions.

    Compute an indexed sum:

    Compute an infinite sum:

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    Applications of Calculus

    Use calculus tools, such as integrals and derivatives, to calculate properties of curves, surfaces, solids and planar regions.

    Compute the area bounded by two curves:

    Locate inflection points of a function:

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    Domain & Range

    Compute the domain and range of real mathematical functions. Plot the domain and range on a number line.

    Compute the domain of a function:

    Compute the range of a function:

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