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The tangent (of a curve) is a vector that is tangent (perpendicular to the normal), i.e. the instantaneous velocity of the curve at a specific point. As such, the initial tangent is the initial velocity of the curve at the point where t=0.

Stated in other terms, the tangent is the slope of the line at a point. This is expressed (in two dimensions, but applicable to higher dimensions), as the line that has x and y coordinates equal to the point of tangency, and slope equal to the limit of delta y over delta x as delta x (and delta y) approaches zero.

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Q: What is initial tangent?
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