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4808pset2ans

# 4808pset2ans - Economics 4808 Problem Set#2 answers 1 Where...

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Economics 4808 Problem Set #2 answers 1. Where is the following function discontinuous? 6 x x 5 x ) x ( f 2 - - - = ; answer: discontinuous at x = -2 and 3. Find the limit: 2. ) 1 x ( 2 x 3 x lim 2 1 x - - + + - = -1 3. lim x x x → - - - 3 3 3 = -1 4. h x f h x f h ) ( ) ( lim 0 - + if x 6 x ) x ( f 2 + = h x h xh x h x f 6 6 2 ) ( 2 2 + + + + = + , so ) 6 2 ( 6 2 ) ( ) ( 2 + + = + + = - + h x h h h xh x f h x f . 6 2 ) 6 2 ( lim 0 + = + + x h h x h h 5. Find f’(x) if 2 3 ) 4 ( 1 ) ( + = x x f ; 3 3 2 ) 4 ( 6 ) ( ' + - = x x x f 6. Find f’(x) if 2 ) 2 ( 1 ) ( + + = x x x f ; 3 4 ) 2 ( ) 2 ( ) 1 )( 2 ( 2 ) 2 ( ) ( ' + - = + + + - + = x x x x x x x f 7. Find f’(x) if 2 3 ) 1 x 6 ( x 2 ) x ( f + = ; ) 1 6 ( 4 ) 1 6 ( 6 ) ( ' 3 2 2 + + + = x x x x x f 8. Find f’(x) if 4 2 3 ) 7 2 ( ) ( - + = x x x f ; ) 4 3 ( ) 7 2 ( 4 ) ( ' 2 3 2 3 x x x x x f + - + = 9. Find f’(x) and the equation to the line tangent to the graph at x=3 if 2 2 ) ( - = x x x f 9 5 - = x y

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10. Find where the line tangent to f(x) is horizontal if 3 2 ) 2 ( ) 4 2 ( ) ( - + + = x x x x f 4 - = x 11. Find f’(x) both by simplifying and by the product rule when f(x) = x 3 (2x 2 +1). Find the derivative: 12. f x e x x x ( ) ( ) = + + 2 4 2 2 ) 4 2 ( ) ( ' ) 4 ( 2 + + = + x e x f x x 13. f x x x ( ) (ln ) = + 2 1 2 2 ) 1 ( ) (ln ) / 1 )( )(ln 1 ( 2 ) ( ' + - + = x x x x x x f 14. f x e x x ( ) ln ( ln ) = + 2 ) 1 1 )( ln ( 2 ) ( ' x x x x f + + = 15. x e x x f 4 2 ) 2 ( ) ( + = x x e x e x x f 4 2 4 ) 2 ( 4 ) 2 ( 2 ) ( ' + + + = 16. The total cost and price (in dollars) for the production and sale of x hats are given by 100 16 ) ( + = x x C x x p 4 . 0 40 ) ( - = a. find the revenue equation and the amount of hats the company must produce to maximize
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4808pset2ans - Economics 4808 Problem Set#2 answers 1 Where...

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