Explanations
Browse explanation pages that build intuition clearly and then connect the idea to notation, graphs, calculators, and formal reasoning.
Showing 4 explanations in Calculus.
What a derivative means geometrically
The derivative is the slope of the tangent line, but that phrase only becomes useful when you compare the curve to nearby secant lines and local linear approximations.
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Why continuity and differentiability are different concepts
Differentiability is stronger than continuity. A graph can be unbroken at a point and still fail to have a derivative there if the local shape has a corner, cusp, or vertical tangent.
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What a Taylor polynomial is approximating
A Taylor polynomial is not trying to copy a function everywhere. It matches the function and several of its derivatives at one chosen center, so it is designed to be locally accurate near that point.
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What the definite integral means geometrically
The definite integral measures signed area between a curve and the -axis. This page builds that idea from Riemann sums, connects it to antiderivatives, and shows how to read integral notation.
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