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2 Pages

### Lecture 2_6MA141

Course: MA 131, Spring 2008
School: N.C. State
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Word Count: 198

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141 Math Lecture Outline for section 2.6 &quot;Tangents, Velocities, and Other Rates of Change) (circles back to material started in 2.1 &quot;The Tangent and Velocity Problems&quot;) We will once again, discuss the slope of secant lines (average rate of change over an interval) and their relationship to slope of tangent line (instantaneous rate of change at a point) Will refer to pictures on page 140...

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141 Math Lecture Outline for section 2.6 "Tangents, Velocities, and Other Rates of Change) (circles back to material started in 2.1 "The Tangent and Velocity Problems") We will once again, discuss the slope of secant lines (average rate of change over an interval) and their relationship to slope of tangent line (instantaneous rate of change at a point) Will refer to pictures on page 140 and 141 of text Two "forms" for the slope Form 1 Slope of secant line connecting points P=(a, f(a)) and Q=(x, f f(x)) (x) f (a) x a Slope of the tangent line at point P=(a, f(a)) f (x) f (a) lim x a x a Example: Look back to example 2.2 page 107 with the slope of the tangent to the curve y = 2^x at point (0,1) Form 2 Slope of tangent line connecting points P and Q P(a, f(a)) and BUT let Q =(a+h, f(a+h)) Slope of secant line f (a h) f (a) f (a h) = a h a h f (a) Slope of the tangent line at point P= (a, f(a)) lim h 0 f (a h) a f (a) Examples #16 Describing the two runners #20 Find the average velocities and instantaneous
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