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Unformatted text preview: y = f ( x ) is called a secant line . If ( a, f ( a ) and ( a + h, f ( a + h )) are two points on the graph of y = f ( x ), we have (slope of secant line from x = a to x = a + h ) = f ( a + h )-f ( a ) ( a + h )-a = f ( a + h )-f ( a ) h . Thus, the slope of secant line can be intercepted as the average rate of change. Example 4. Given y = f ( x ) = x 2 , (a) Find the slope of secant line for a = 1, and h = 2 and 1, respectively. (b) Find the slope of secant line for a = 1 and h for any nonzero number. (c) Find the limit of expression in part (2) as h → 0. Deﬁnition 3. Given y = f ( x ), the slope of the tangent line of f ( x ) at the point x = a is given by lim h → f ( a + h )-f ( a ) h if the limit exists. 2...
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