M-273Q Midterm: MATH 273 Montana State OldExam1

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15 Feb 2019
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▼✷✼✸◗ ▼✉❧t✐✈❛r✐❛❜❧❡ ❈❛❧❝✉❧✉s ❖❧❞ ❊①❛♠ ✶
◆❛♠❡ ❛♥❞ s❡❝t✐♦♥✿
■♥str✉❝t♦r✬s ♥❛♠❡✿
■♥str✉❝t✐♦♥s ❈❧♦s❡❞ ❜♦❦✳ ◆♦ ❝❛❧❝✉❧❛t♦r ❛❧❧♦✇❡❞✳ ❉♦✉❜❧❡✲s✐❞❡❞ ❡①❛♠✳ ◆❖ ❈❊▲▲ P❍❖◆❊❙✳
❙❤♦✇ ❛❧❧ ✇♦r❦ ❛♥❞ ✉s❡ ❝♦rr❡❝t ♥♦t❛t✐♦♥ t♦ r❡❝❡✐✈❡ ❢✉❧❧ ❝r❡❞✐t✦ r✐t❡ ❧❡❣✐❜❧②
s✮ ❂
❞s
✮ ❂ ✵✵
❬✶ ✰ ✭✮✮
t✮ ❂ ❥❥t❥❥
❥❥rt❥❥ t✮ ❂ ❥❥rtr✵✵t❥❥
❥❥rt❥❥
✶✳ ✭✶ ❝r❡❞✐t ❉❡❝✐❞❡ ✇❤❡t❤❡r t❤❡ ❢♦❧❧♦✇✐♥❣ q✉❛♥t✐t✐❡s ❛r❡ ✈❡❝t♦rs✱ s❝❛❧❛rs✱ ♦r ❛r❡ ♥♦♥s❡♥s✐❝❛❧ ✭t❤❛t ✐s✱
t❤❡ st❛t❡♠❡♥t ✐s ♥♦t ❞❡☞♥❡❞ ♦r ❞♦❡s ♥♦t ♠❛❦❡ s❡♥s❡✮
❡❝t♦r ❙❝❛❧❛r ◆♦♥s❡♥s❡ ✭
❡❝t♦r ❙❝❛❧❛r ◆♦♥s❡♥s❡
❡❝t♦r ❙❝❛❧❛r ◆♦♥s❡♥s❡ ✭
❡❝t♦r ❙❝❛❧❛r ◆♦♥s❡♥s❡ t✮ ❂ ❥❥rtr✵✵ t❥❥
❥❥rt❥❥
✷✳ ✭✶ ❝r❡❞✐t ❉❡t❡r♠✐♥❡ ✇❤❡t❤❡r t❤❡ ❢♦❧❧♦✇✐♥❣ ❡q✉❛t✐♦♥s ❞❡s❝r✐❜❡ ❛ ♣❧❛♥❡✱ ❛ ❧✐♥❡✱ ♦r ♥❡✐t❤❡r ✐♥
P❧❛♥❡ ▲✐♥❡ ◆❡✐t❤❡r rt✮ ❂t ❁
P❧❛♥❡ ▲✐♥❡ ◆❡✐t❤❡r ❂ ✶
P❧❛♥❡ ▲✐♥❡ ◆❡✐t❤❡r ✺ ✰
P❧❛♥❡ ▲✐♥❡ ◆❡✐t❤❡r t ✼ ✰ ✷t❀ ②t ✶✶ t❀ ③t✮ ❂ t
✸✳ ✭✶ ❝r❡❞✐t ❋✐♥❞ ❛ ✉♥✐t ❡❝t♦r ♣❛r❛❧❧❡❧ t♦ t❤❡ ❧✐♥❡ rt✮ ❂ t ✰ ✹✷ ✰ ✷t❀ t ❃ ✿
Pr♦❜❧❡♠ ✸ ❚♦t❛❧
❈r❡❞✐t ✶ ✶ ✶
●P❆ ❈r❡❞✐t P♦✐♥ts ❊❛r♥❡❞
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▼✷✼✸◗ ▼✉❧t✐✈❛r✐❛❜❧❡ ❈❛❧❝✉❧✉s ❖❧❞ ❊①❛♠ ✶ ✲ P❛❣❡ ✷ ♦❢ ✽
✹✳ ▲❡t ❛♥❞ ❃ ✿
✭❛✮ ✭✶ ❝r❡❞✐t ❋✐♥❞
✭❜✮ ✭✶ ❝r❡❞✐t ❋✐♥❞
✭❝✮ ✭✶ ❝r❡❞✐t ❋✐♥❞
✭❞✮ ✭✶ ❝r❡❞✐t ❋✐♥❞ ✸
✭❡✮ ✭✶ ❝r❡❞✐t ■s t❤❡ ❛♥❣❧❡ ❡t✇❡❡♥ ❛♥❞ ❛❝✉t❡ ✭❧❡ss t❤❛t ✷✮✱ ♦❜t✉s❡ ✭❣r❡❛t❡r t❤❛♥ ✷✮✱ ♦r
♥❡✐t❤❡r❄
Pr♦❜❧❡♠ ✹ ❚♦t❛❧
❈r❡❞✐t ✺ ✺
●P❆ ❈r❡❞✐t P♦✐♥ts ❊❛r♥❡❞
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▼✷✼✸◗ ▼✉❧t✐✈❛r✐❛❜❧❡ ❈❛❧❝✉❧✉s ❖❧❞ ❊①❛♠ ✶ ✲ P❛❣❡ ✸ ♦❢ ✽
✺✳ ✭✶ ❝r❡❞✐t ❋✐♥❞ ❛ ✈❡❝t♦r ♦❢ ❧❡♥t❤ t❤❛t ✐s ♦rt❤♦❣♦♥❛❧ t♦ ❜♦t❤ ❛♥❞ ❃ ✿
✻✳ ❚❤✐s q✉❡st✐♦♥ ❤❛s t✇♦ ♣❛rts✳
✭❛✮ ✭✶ ❝r❡❞✐t ❋✐♥❞ t❤❡ ❡q✉❛t✐♦♥ ♦❢ t❤❡ ❧✐♥❡ t❤r♦✉❣❤ P✭✸✵✮ ❛♥❞ ✭✶✸✮
✭❜✮ ✭✶ ❝r❡❞✐t ❙❤♦✇ t❤❛t t❤❡ ❧✐♥❡ ②♦✉ ❢♦✉♥❞ ✐♥ ♣❛rt ✭❛✮ ✐s ♦rt❤♦❣♦♥❛❧ t♦ t✮ ❂ ✸t❀ ②t✮ ❂ ✸✰t❀ ③t✮ ❂
✼ ✰ ✻t✿
✼✳ ✭✷ ❝r❡❞✐t ❋✐♥❞ ❛♥ ❡q✉❛t✐♦♥ ❢♦r t❤❡ t❛♥❣❡♥t ❧✐♥❡ t♦ t❤❡ ❝✉r✈❡ rt✮ ❂ t❀ t❀ t❛t t❤❡ ♣♦✐♥t ✭✶✶✮
Pr♦❜❧❡♠ ✼ ❚♦t❛❧
❈r❡❞✐t ✶ ✷ ✷
●P❆ ❈r❡❞✐t P♦✐♥ts ❊❛r♥❡❞
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