EC14C_Problem_Set_6_-_updated - 1 , 3 1 , 8 1 , 1 3 ) ( 2 x...

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1 EC14C Problem Paper # 6 Limits and Continuity In Exercises 1-10, find the limits, if they exist. 1. ) 3 ( lim 2 x x 2. 4 lim 12 x 3. 3 9 lim 2 3 x x x 4. 2 4 4 lim 2 2 x x x x 5. 3 2 3 2 2 4 lim x x x x x 6. h x h x h 2 2 0 2 ) ( 2 lim 1 , 2 1 , 1 6 ) ( where ) ( lim . 7 2 1 x x x x x f x f x 8. x x x x 3 3 3 1 2 lim 9. 1 1 4 lim 2 x x x 10. 1 6 5 3 lim 2 x x x x 11. The cost C of removing p percent of the particulate pollution from the smoke stacks of an industrial plant is given by p p p C 100 7300 ) ( . (a) Find ) ( lim 100 p C p , if it exists (b) Can 100% of the particulate pollution be removed? Why? 12. If 2 , 3 8 2 , ) ( 2 x x x x x x f , is f continuous at x = 2? Give reasons. 13. If 2 , 7 4 2 , 3 ) ( x x x x x f , is f continuous at x = 2? Give reasons. 14. If
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Unformatted text preview: 1 , 3 1 , 8 1 , 1 3 ) ( 2 x x x x x x f , is f continuous at x = 1? Give reasons. In Exercises 15-17, determine the points at which the rational function is discontinuous. 15. 25 6 ) ( 2 x x x f 16. 12 1 2 ) ( 2 x x x x f 17. x x x x f 2 2 1 ) ( 18. Suppose that the cost C of removing p percent of the impurities from the waste water in a manufacturing process is given by p p p C 101 9800 ) ( . Is this function continuous for all those p-values for which the problem makes sense?...
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