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165s10spec4

# 165s10spec4 - in billions is Year 1990 2002 GDP in billions...

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Math 165, Spring 2010, Lowman Special Assignment #4 Part I Integration Write the general forms of the Power Rule, Exponential Rule and Log Rule for derivatives. Write the general forms of the Power Rule, Exponential Rule and Log Rule for integrals. Find the following integrals. Use the general forms of the power, exponential and log rules. Do not use the method of substitution. You must show your work to receive credit. 1 . R 5 e 3 x + 1 3 x - 1 2 x 3 / 2 dx 2 . R (3 x + 4) 5 dx 3 . R 4 x 3 dx 4 . R 5 x 4 +4 x 3 - 10 x 3 dx 5 . R e 5 x dx 6 . R 1 3 x +5 dx 7 . R [( x - 1) 5 + 3( x - 1) 2 + 5] dx 8 . R 2 xe x 2 - 1 dx 9 . R 3 t t 2 + 8 dt 10 . R x 5 e 1 - x 6 dx 11 . R y 2 ( y 3 +5) 2 dy 12 . R (3 x 2 - 1) e x 3 - x dx 13 . R 10 x 3 - 5 x x 4 - x 2 +6 14 . R 1 x ln x dx 15 . R 6 u - 3 4 u 2 - 4 u +1 du 16 . R ln x 2 x dx 17 . R e x x dx

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Part II Logarithms and Exponentials 1. Write down all of the Log Rules used this semester and give an example of each. 2. An economist has compiled the following data on the gross domestic product (GDP) of a certain country. Use these data to predict the GDP in the year 2010 if the GDP is increasing exponentially. GDP
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Unformatted text preview: in billions is: Year 1990 2002 GDP in billions 100 150 (a) 197 billion (b) 225 billion (c) 365 billion (d) 150 billion (e) 300 billion 3. Use logarithmic dierentiation to nd f ( x ) at x = 1 if f ( x ) = (2 + 3 x ) x . (a) 10.05 (b) 11.05 (c) 18.05 (d) 21.05 (e) 24.31 4. Solve the following equation for x. Give your answer to 4 decimal places. Show your work. ln(4 e x ) + ln(2 e 3 x ) = ln(16) (a) .4545 (b) .1733 (c) .3660 (d) .1111 (e) .2310 5. How many years will it take \$1000 to grow to \$1 , 000 , 000 if com-pounded quarterly at invested at 10% per year? (a) 130.6 years (b) 25.3 years (c) 69.9 years (d) 73.2 years (e) 87.2 years 6. Repeat the preveous problem if it is compounded continuously. 7. Find log 1 . 4 100 . 736 . Use your calculator....
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165s10spec4 - in billions is Year 1990 2002 GDP in billions...

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