MAT135H1 Chapter 2.1: Calculus 8E Section 2.1 Notes

• School: UTSG
• Department: Mathematics
• Course: MAT135H1
• Professor: natalia Christina Garcia

Document Summary

Mat135h1 f - calculus 8th edition (stewart) - section 2. 1 - the tangent and velocity. Tangent to a curve is a line that touches the curve / has the same slope as the curve at the point of contact. Not always true that the tangent intersects the circle once and only once: l intersects the curve only once, but is obviously not a tangent; t is a tangent, but intersects c twice. Since the tangent is linear, we can find a tangent line t with slope m to find the tangent at point p. Since mpq x 2 1 x 1. As q approaches p (i. e. x approaches 1), slope of t approaches 2. Can thus say that the slope of the t is the limit of the slopes of the secant lines. Thus, assuming the slope is indeed 2, the tangent can be expressed as y 1 = 2 x 1 y = 2x 1.