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Unformatted text preview: TANGENT AND VELOCITY In elementary geometry, the line tangent to a circle at a point p is the line through p that intersects the circle only at the point p . For a general plane curve, however, this is not true. In fact, the only way to describe a tangent line is to examine the shape of the curve near the point. We will see the definition of a tangent line a few weeks later. Right now, we just say that a line is tangent to a curve at a point if the line is a limit of secant lines that pass through the point at which the tangent line intersects the curve and the other point that becomes closer to the first point. Example 1. Find an equation of the tangent line to the graph of y = x 3 at the point P (1 , 1). Solution Since we already know the tangent line passes through (1 , 1), we only need to know the slope of the line. After that, we can use the point-slope form of the equation of a line....
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This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.
- Fall '09