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Pre-Calc Homework Solutions 221

# Pre-Calc Homework Solutions 221 - Section 5.4 3 2 221 21(a...

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21. (a) No, f ( x ) 5 tan x is discontinuous at x 5 } p 2 } and x 5 } 3 2 p } . (b) The integral does not have a value. If 0 , b , } p 2 } , then E b 0 tan x dx 5 3 2 ln ) cos x ) 4 5 2 ln ) cos b ) since the Fundamental Theorem applies for [0, b ]. As b } p 2 } 2 , cos b 0 1 so 2 ln ) cos b ) or E b 0 tan x dx . Hence the integral does not exist over a subinterval of [0, 2 p ], so it doesn’t exist over [0, 2 p ]. 22. (a) No, f ( x ) 5 } x x 2 1 2 1 1 } is discontinuous at x 5 1. (b) The integral does not have a value. If 0 , b , 1, then E b 0 } x x 2 1 2 1 1 } dx 5 E b 0 } x 2 1 1 } dx 5 3 ln ) x 2 1 ) 4 5 ln ) b 2 1 ) , since } x x 2 1 2 1 1 } 5 } x 2 1 1 } and the Fundamental Theorem applies for [0, b ]. As b 1 2 , ln ) b 2 1 ) 2‘ or E b 0 } x x 2 1 2 1 1 } dx 2‘ . Hence the integral does not exist over a subinterval of [0, 2], so it does not exist over [0, 2]. 23. (a) No, f ( x ) 5 } sin x x } is discontinuous at x 5 0. (b) NINT 1 } sin x x } , x , 2 1, 2 2 < 2.55. The integral exists since the area is finite because } sin x x } is bounded.
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