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 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 one-sided limit:

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Products

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

#### Compute an infinite product:

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Vector Analysis

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

#### 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.

#### 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.

#### 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.

#### Solve a recurrence:

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Series Expansions

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

#### 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.

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### GO FURTHER

Step-by-Step Solutions for CalculusCalculus Web AppFree Unlimited Calculus Practice Problems

### RELATED EXAMPLES

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

• Wolfram Calculus & Algebra
• Wolfram Calculus Guide Page
• 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 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.

#### 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 range of a function:

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