Pre-Calc Homework Solutions 70

Pre-Calc Homework Solutions 70 - 70 Section 3.1 f (3 1...

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Quick Review 3.1 1. lim h 0 } (2 1 h 4 ) 2 2 4 } 5 lim h 0 } (4 1 4 h 1 h h 2 ) 2 4 } 5 lim h 0 4 1 h 5 4 1 0 5 4 2. lim x 2 + } x 1 2 3 } 5 } 2 1 2 3 } 5 } 5 2 } 3. Since } ) y y ) }52 1 for y , 0, lim y 0 2 } ) y y ) }52 1. 4. lim x 4 } ˇ 2 x x w 2 2 8 2 } 5 lim x 4 5 lim h 4 2( ˇ x w 1 2) 5 2( ˇ 4 w 1 2) 5 8 5. The vertex of the parabola is at (0, 1). The slope of the line through (0, 1) and another point ( h , h 2 1 1) on the parabola is } ( h 2 h 1 2 1) 0 2 1 }5 h . Since lim h 0 h 5 0, the slope of the line tangent to the parabola at its vertex is 0. 6. Use the graph of f in the window [ 2 6, 6] by [ 2 4, 4] to find that (0, 2) is the coordinate of the high point and (2, 2 2) is the coordinate of the low point. Therefore, f is increasing on ( 2‘ , 0] and [2, ). 7. lim x 1 1 f ( x ) 5 lim x 1 1 ( x 2 1) 2 5 (1 2 1) 2 5 0 lim x 1 2 f ( x ) 5 lim x 1 2 ( x 1 2) 5 1 1 2 5 3 8. lim h 0 1 f (1 1 h ) 5 lim x 1 1 f ( x ) 5 0 9. No, the two one-sided limits are different (see Exercise 7). 10.
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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