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Exam2_3 6 - Version 208 Exam 2 Radin(58305 5 33 4 limit =...

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Version 208 – Exam 2 – Radin – (58305) 6 5. bracketleftBig π 3 , π 3 bracketrightBig 6. bracketleftBig π , π 3 bracketrightBig , bracketleftBig π 3 , π bracketrightBig correct Explanation: After differentiation, f ( x ) = 2 cos x 1 . Now f will be decreasing on an interval [ a, b ] if f ( x ) < 0 on ( a, b ). But for x in ( π, π ), f ( x ) = 2 cos x 1 = 0 when x = π/ 3 , π/ 3. Thus the graph -1 -2 -3 1 π π π 4 π 4 π 2 π 2 3 π 4 3 π 4 of f on ( π, π ) shows that f ( x ) < 0 only on parenleftBig π , π 3 parenrightBig , parenleftBig π 3 , π parenrightBig . Consequently, f will be decreasing only on the intervals bracketleftBig π , π 3 bracketrightBig , bracketleftBig π 3 , π bracketrightBig . 013 10.0 points Determine if the limit lim x → −∞ 1 + 2 x 5 x 3 3 + 2 x 3 exists, and if it does, find its value. 1. limit = 5 2 2. limit does not exist 3. limit = 1 3 4. limit = 1 3 5. limit = 5 2 correct Explanation: Dividing by
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