Examples for

Applications of Calculus

The tools of calculus can be used in a variety of applications to compute properties and to describe the behavior of functions, curves, surfaces, solids and many other mathematical objects. Harness Wolfram|Alpha's comprehensive computational understanding of limits, derivatives and integrals to find asymptotes, tangents and normals of curves; compute arc length; find the singular and stationary points of functions; and beyond.

Asymptotes

Compute horizontal, vertical or slant asymptotes.

Compute asymptotes of a function:

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Cusps & Corners

Compute and visualize cusps and corners of a function.

Find cusps on the graph of a function:

Find corners on the graph of a function:

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Optimization

Find global and local extrema and stationary points of functions or impose a constraint on a function and compute the constrained extrema.

Minimize or maximize a function:

Minimize or maximize a function of several variables:

Minimize or maximize a function subject to a constraint:

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Surfaces & Solids of Revolution

Compute the area of a surface of revolution or compute the volume of a solid of revolution.

Compute properties of a surface of revolution:

Compute properties of a solid of revolution:

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Tangents & Normals

Compute a tangent line to a curve or compute a tangent plane or a normal line to a surface.

Find the tangent to the graph of a function at a point:

Find the normal to a curve specified by an equation:

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Stationary Points

Compute and visualize stationary points of a function.

Locate stationary points of a function:

Find stationary points of a function of several variables:

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Area between Curves

Compute the areas of enclosed regions, bounded regions between intersecting points or regions between specified bounds.

Compute the area bounded by two curves:

Specify limits on a variable:

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Curvature

Compute the curvature of functions and parameterized curves in various coordinate systems and dimensions.

Compute the curvature of a plane curve:

Compute the curvature of a space curve at a point:

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RELATED EXAMPLES

  • Applied Mathematics
  • Plotting & Graphics
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  • Inflection Points

    Compute and visualize inflection points of a function.

    Locate inflection points of a function:

    Find inflection points in a specified domain:

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    Arc Length

    Compute arc lengths in various coordinate systems and dimensions.

    Compute the arc length of a curve:

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    Saddle Points

    Compute and visualize saddle points of a function.

    Locate saddle points of a function:

    Find the saddle point nearest to a specified point:

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