SECTION 12.4 The Limit of a Sequence; Infinite Series 887 116. Find the value of the determinant: − − − 3 1 0 0 2 6 4 1 2 117. Liv notices a blue jay in a tree. Initially she must look up 5 degrees from eye level to see the jay, but after moving 6 feet closer she must look up 7 degrees from eye level. How high is the jay in the tree if you add 5.5 feet to account for Liv’s height? Round to the nearest tenth. 118. Write the factored form of the polynomial function of smallest degree that touches the x -axis at x 4, = crosses the x -axis at x 2 = − and x 1, = and has a y -intercept of 4. 119. Given s t t t 16 3 , 2 ( ) = − + find the difference quotient s t s t 1 1 . ( ) ( ) − − 120. Find a rectangular equation of the plane curve with parametric equations x t t y t t t 5 and for 0 ( ) ( ) = + = ≥ 121. Find the function g whose graph is the graph of y x = but is stretched vertically by a factor of 7 and shifted left 5 units. 122. Factor completely: x x 29 100 4 2 − + ‘Are You Prepared?’ Answer 1. 0.013125 12.4 The Limit of a Sequence; Infinite Series OBJECTIVES 1. Find the Limit of a Sequence (p. 887) 2. Define Infinite Series and Geometric Series (p. 889) 1 Find the Limit of a Sequence Consider the sequence { } { } = + s n n 2 1 . n The terms of this sequence are … 1, 4 3 , 3 2 , 8 5 , 5 3 , Figure 17 shows the graph of the sequence. Figure 17 { } { } = + s n n 2 1 n 20 12 4 0 2 1 16 8 y 5 2 y x Notice that the points on the graph are getting closer to the line = y 2. To see why, consider the following: + = ⋅ + = ⋅ + n n n n n 2 1 2 1 2 1 1 1 Divide the numerator and denominator by n.
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