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.
Compute definite and indefinite integrals of functions. Integrate with respect to one or more variables.
Compute an indefinite integral:
integrate x^2 sin^3 x dxCompute a definite integral:
integrate sin x dx from x=0 to piCompute an improper integral:
int sinx/x dx, x=0..infinityExplore the limit behavior of a function as it approaches a single point or asymptotically approaches infinity.
Compute a limit:
lim (sin x - x)/x^3 as x->0limit (1+1/n)^n as n->infinityCompute a one-sided limit:
lim x/|x| as x->0+Compute an indexed product by multiplying a finite or infinite number of terms.
Compute an indexed product:
product (k+2)/k, k=1..25Compute an infinite product:
product (1-1/n^4), n=2 to infinityApply the curl, the gradient and other differential operators to scalar and vector fields.
Compute the gradient of a function:
grad sin(x^2 y)Calculate alternate forms of a vector analysis expression:
curl (curl F)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:
is sin(x-1.1)/(x-1.1)+heaviside(x) continuousLocate discontinuities of a function:
discontinuities (x^3+8)/(x^3+3x^2-4x-12)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:
derivative of x^4 sin xCompute higher derivatives:
second derivative of sin(2x)Compute partial derivatives:
d/dx x^2 y^4, d/dy x^2 y^4Calculate and examine sequences of integers or other numerical values. Find continuations and formulas for known or unknown sequences.
Analyze a sequence:
sequence of Fibonacci numbersCompute a possible formula and continuation for a sequence:
1, 4, 9, 16, 25, ...Solve a recurrence:
g(n+1)=n^2+g(n)Find Taylor series, Laurent series and more about any point.
Find a Taylor series expansion:
taylor series sin xSpecify the center point and the order of the expansion:
series (sin x)/(x-pi) at x=pi to order 10Calculate the Fourier transform, Laplace transform and other integral transforms of functions.
Compute a Fourier transform:
Fourier transform exp(-x^2)Compute a Laplace transform:
LT e^t sin 2tGO FURTHER
Step-by-Step Solutions for CalculusCalculus Web AppFree Unlimited Calculus Practice ProblemsRELATED EXAMPLES
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Compute the value of indexed summations, or sums of sequences of values. Compute infinite sums and find convergence conditions.
Compute an indexed sum:
sum j^2, j=1 to 100Compute an infinite sum:
sum (3/4)^j, j=0..infinityUse calculus tools, such as integrals and derivatives, to calculate properties of curves, surfaces, solids and planar regions.
Compute the area bounded by two curves:
compute the area between y=|x| and y=x^2-6Locate inflection points of a function:
inflection points of x+sin(x)Compute the domain and range of real mathematical functions. Plot the domain and range on a number line.