Interactive Calculus Simulations
Calculus Starships' interactive simulations let you drag, rotate, and explore the hardest AP and college calculus concepts — related rates, volumes of revolution, polar area, derivatives, and limits — instead of memorizing them from static formulas. Each guide pairs a visual simulator with the formula and a worked example.
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Graphical Limits guide →
Graphical Limits
Visualize and solve one-sided and two-sided limits using interactive graphs. Master continuity and limits in calculus st...
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Graphical Derivatives guide →
Graphical Derivatives
Explore how the slope of a tangent line maps directly to the derivative function graph. Drag points and inspect rate of ...
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The Power Rule guide →
The Power Rule
Learn the fundamental derivative shortcut. Slide parameters and see how polynomials differentiate visually in real-time....
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The Product Rule guide →
The Product Rule
Learn how to differentiate the product of two functions. Explore step-by-step visual models of f(x)g(x) derivatives....
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The Quotient Rule guide →
The Quotient Rule
Visualize fractions of functions and compute derivatives. Learn the quotient rule mnemonic with our interactive guide....
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Related Rates guide →
Related Rates
Master related rates word problems in calculus. Learn how to identify shapes, plug in constants, and take implicit deriv...
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Definite Integrals guide →
Definite Integrals
Learn how definite integrals calculate the area under a curve. Move from simple geometry to integration with our interac...
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Volume of Rotation guide →
Volume of Rotation
Revolve single functions around axis lines. Visualize solid disk volumes in 3D space with our step-by-step calculus guid...
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Volume of Rotation guide →
Volume of Rotation
Visualize rotating region functions around any axis. Master disk and washer method concepts with our interactive step-by...
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Volume of Rotation guide →
Volume of Rotation
Explore how revolving functions around non-x and non-y axes (y = k or x = h) changes volume integrals with our interacti...
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Area Bounded by Polar Curves guide →
Area Bounded by Polar Curves
Learn how to calculate the area bounded by polar curves. Plot polar graphs, understand polar coordinates, and visualize ...
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Area Between Polar Curves guide →
Area Between Polar Curves
Find intersection angles and calculate the area between polar curves (e.g. cardioid and circle) using our interactive po...
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Choosing a Convergence Test guide →
Choosing a Convergence Test
Which convergence test should you use? Run this ordered checklist: nth-term, recognize the form, factorials to the ratio...
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Choosing u for U-Substitution guide →
Choosing u for U-Substitution
Stuck on u-substitution? Set u to the inside function whose derivative is also a factor in the integrand. Get the rule, ...
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Choosing an Integration Technique guide →
Choosing an Integration Technique
How to know which integration technique to use: an ordered checklist (rewrite, u-sub, parts, partial fractions, trig sub...