In calculus, you’ll often hear “The derivative is the slope of the tangent line.” But what is a tangent line? The definition is trickier than you might think. Tangent lines are important because they are the best way to approximate a curve using a line. We can then use the slope of the line as a way to measure the “slope” of the curve.
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Calculus is the mathematical study of curves in the plane, surfaces in space, and other "non flat" shapes. You learn about the derivative, which describes how quickly a curve is changing at a specific point. You will also study the integral, which combines the values of a curvy object over a region. While these may seem like opposite puzzles, they are actually connected! So get ready to leave the world of lines behind as you begin to learn the tools needed to study more fancy shapes.