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### 319handout1

Course: ECON 3190, Fall 2008
School: Cornell
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Word Count: 202

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319, Econ Fall 2008 TA: Simon Kwok Handout 1 Dierentiation: 1. Compute the derivatives y 0 . (a) y = 3x7 + 5x (b) y = x2 8x + 4 8x + 4) (c) y = (3x7 + 5x)(x2 (d) y = 3x7 +5x x2 8x+4 (e) y = (3x7 + 5x)10 (f) y = p x x2 8x+4 x2 8x+4 (g) y = e (h) y = ln(x2 (i) y = ln ln x (j) y = ee x 8x + 4) (k) y = sin(3x7 + 5x) 2.(a) Compute the rst two derivatives of f (x) = (b) Where is the maximum of f (x) attained? 3....

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319, Econ Fall 2008 TA: Simon Kwok Handout 1 Dierentiation: 1. Compute the derivatives y 0 . (a) y = 3x7 + 5x (b) y = x2 8x + 4 8x + 4) (c) y = (3x7 + 5x)(x2 (d) y = 3x7 +5x x2 8x+4 (e) y = (3x7 + 5x)10 (f) y = p x x2 8x+4 x2 8x+4 (g) y = e (h) y = ln(x2 (i) y = ln ln x (j) y = ee x 8x + 4) (k) y = sin(3x7 + 5x) 2.(a) Compute the rst two derivatives of f (x) = (b) Where is the maximum of f (x) attained? 3. We want to nd the value of that maximizes g( ) = p1 2 p1 2 e (x 1)2 2 . e (1 2 )2 p1 2 e (3 2 )2 p1 2 e (5 2 )2 . (a) obtain First the expression L( ) = ln g( ). (b) Show that L( ) is an increasing function of g( ). (c) Find the value of that maximizes g( ). Integration: 4. Compute the following indenite integrals: Z (a) (4x6 + 2x3 + 1)dx Z px (b) dx x2 +1 Z x2 (c) (x3 +7)3 dx Z 1 (d) 1+x2 dx (Hint: substitute using the tan function) 1 (e) (f) Z Z p1 dx 4 x2 (Hint: substitute using the sin function) xe x dx (Hint: integration by parts) 5. Compute the following denite integrals: Z5 e x dx (a) 0 Z 10 1 (b) x dx 1 Z3 (c) 5 xe 5x dx 0 2
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