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:
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:
Compute fractional derivatives, integrals and differintegrals.
Compute a Caputo fractional differintegral:
Compute a fractional derivative:
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:
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:
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:
Compute an indexed product by multiplying a finite or infinite number of terms.
Compute an indexed product:
Compute an infinite product:
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:
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:
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:
Calculate the Fourier transform, Laplace transform and other integral transforms of functions.
Compute a Fourier transform:
Compute a Laplace transform:
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:
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: