2.2 Class Notes

2.2 Class Notes - The first question on the prelim (4...

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The first question on the prelim (4 points) Write your name and section number on your paper. There will be three word problems (not counting this one) Equation of the tangent line 1/3 Find the equation of the tangent line to () at 216. Use the tangent line to estimate (225) Give the answer to four decimal places fx x x = = 00 0 () ' ( ) yf x f xx x = +− 2/3 2 000 ( ) '( ) (1/3) 216 ( ) 6 '( ) 1/(3 6 ) 1/108 6 ( 216) /108 91 (225) 6 6 6.0833 108 12 (225) exp((1/ 3)ln(225)) 6.0822 f x x xf x f x yx == = = =+ − ≈+ =+ = Monkeyface prickelback /4 2.5 16(1 ) inches 0.01 pounds Find / t Le WL dW dt =− = 2.5 1.5 1.5 /4 1.5 ) 0.01 / 0.025 / (16)(1/ 4) / 0.025[16(1 )] 4 0.64(1 ) t t tt W L dW dL L dL dt e dW dt e e ee −− = = = dW dW dL dt dL dt =⋅ Solution 2 2.5 ) inches 0.01 pounds Find / ( ) 0.01(16(1 )) '( ) 0.01(2.5)(16(1 )) (4 ) 0.64(1 ) t t dW dt Wt e e e =
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At what time does the m.p. reach ½ of its final length of 32 inches? How fast is the weight growing at that time? /4 /4 1.5 32(1 ) /0 . 6 4 ( 1 ) t tt Le dW dt e e −− =− Answers 2.5 16(1 8 at time 4ln 2 2.772 years / 0.64(1 ) 0.64(1/ 2) t Lt dW dt e e == = = NSF Budget As part of the American Competitiveness Act
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This note was uploaded on 11/14/2007 for the course MATH 1106 taught by Professor Durrett during the Spring '07 term at Cornell.

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2.2 Class Notes - The first question on the prelim (4...

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