Calculus
Calculus is the mathematics of change and accumulation. These tools cover the central operations — differentiation, integration, limits and tangent lines — with exact symbolic answers for polynomials and accurate numeric methods for any other function.
Every calculus tool here builds on three core ideas: a derivative measures the instantaneous rate of change, an integral accumulates a quantity, and a limit captures what a function approaches near a point. The polynomial tools give exact symbolic answers; the general-function tools use numeric methods with clearly stated precision.
Polynomial derivatives and integrals
For polynomials the power rule and its reverse give exact answers term by term. The two polynomial tools show every step and accept a definite-integral interval when you want F(b) − F(a).
Numeric derivatives
For any function of x, the central-difference derivative estimates f'(a) using values close to the point. It is accurate to several significant figures for smooth functions.
Definite integrals
The definite integral solver uses composite Simpson's rule with 1000 subintervals — accurate even for curves where pure midpoint or trapezoidal methods struggle.
Limits and tangent lines
The limit tool samples both sides of the target and reports when the two agree; the tangent line tool returns both point-slope and slope-intercept forms of the tangent at a point.
All solvers
Frequently asked questions
Are the answers exact?
The polynomial tools are symbolic and exact. The general-function tools are numeric — clearly marked with ≈ — and accurate to many significant figures.
What method does the numeric integral use?
Composite Simpson's rule with 1000 subintervals, which fits the curve with parabolic segments for high accuracy.
Can it handle a removable hole in a limit?
Yes. The limit tool samples points close to but not at the target, so it finds the limiting value even when the function is technically undefined there.