Tangent 1
In geometry, the tangent line (or simply tangent) to a plane curve at a given Point (geometry), point is, intuitively, the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitesimal, infinitely close points on the curve. More precisely, a straight line is tangent to the curve at a point if the line passes through the point on the curve and has slope , where ''f'' is the derivative of ''f''. A similar definition applies to space curves and curves in ''n''-dimensional Euclidean space. The point where the tangent line and the curve meet or intersection (geometry), intersect is called the ''point of tangency''. The tangent line is said to be "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also be thought of as a ''tangent line approximation'', the graph of the affine function that best ap ...
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