319handout1 - (a) Z (4 x 6 + 2 x 3 + 1) dx (b) Z x p x 2 +1...

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Econ 319, Fall 2008 TA: Simon Kwok Handout 1 Di/erentiation: 1. Compute the derivatives y 0 . (a) y = 3 x 7 + 5 x (b) y = x 2 8 x + 4 (c) y = (3 x 7 + 5 x )( x 2 8 x + 4) (d) y = 3 x 7 +5 x x 2 8 x +4 (e) y = (3 x 7 + 5 x ) 10 (f) y = x p x 2 8 x +4 (g) y = e x 2 8 x +4 (h) y = ln( x 2 8 x + 4) (i) y = ln ln x (j) y = e e x (k) y = sin(3 x 7 + 5 x ) f ( x ) = 1 p 2 e ( x 1) 2 2 . (b) Where is the maximum of f ( x ) attained? that maximizes g ( ) = 1 p 2 e (1 ) 2 2 ± 1 p 2 e (3 ) 2 2 ± 1 p 2 e (5 ) 2 2 . (a) First obtain the expression L ( ) = ln g ( ) . (b) Show that L ( ) is an increasing function of g ( ) . (c) Find the value of that maximizes g ( ) . Integration:
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Unformatted text preview: (a) Z (4 x 6 + 2 x 3 + 1) dx (b) Z x p x 2 +1 dx (c) Z x 2 ( x 3 +7) 3 dx (d) Z 1 1+ x 2 dx (Hint: substitute using the tan function) 1 (e) Z 1 p 4 & x 2 dx (Hint: substitute using the sin function) (f) Z xe & x dx (Hint: integration by parts) 5. Compute the following de&nite integrals: (a) Z 5 e & x dx (b) Z 10 1 1 x dx (c) 5 Z 3 xe & 5 x dx 2...
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319handout1 - (a) Z (4 x 6 + 2 x 3 + 1) dx (b) Z x p x 2 +1...

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