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A few examples of what you can ask Wolfram|Alpha about:
do basic arithmetic
do exact arithmetic with fractions
compute a decimal approximation of a specified number of digits
convert a decimal number to another base
plot a function
plot a region satisfying multiple inequalities
solve an equation
factor a polynomial
compute eigenvalues and eigenvectors of a matrix
compute an integral
calculate a derivative
solve an ordinary differential equation
compute properties of a geometric figure
plot a conic section and identify its type
compute properties of a polyhedron
compute a prime factorization
solve a Diophantine equation
compute a possible formula and continuation for a sequence
analyze a graph specified by adjacency rules
solve a recurrence
minimize or maximize a function
numerically integrate functions that cannot be integrated symbolically
do computations with special functions
do computations with number-theoretic functions
find representations for a function
compute properties of a function of a complex variable (use the variable z)
do vector analysis computations
compute properties of a knot
find information about a math concept
get a brief definition
get information about a mathematical conjecture
get historical information about a theorem
find the continued fraction representation of a number
find definitions of continued fraction terminology
find continued fraction papers by author
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