126RECEX3 - f ( x ) = ( x 5 + 7 x + 1) 4 (3 x 2 + e 2 x +...

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MAT 126: Calculus B — Recitation Exercise Sheet #3, Fall 2009 1. State the following rules for differentiation. (a) Product Rule (b) Quotient Rule (c) Chain Rule (d) Logarithm and Exponential of the form a x (e) Trigonometric Functions (f) Inverse Trigonometric Functions (g) Polynomial Functions of the form p ( x ) = n k =0 a k x k . 2. For each of the following, find the derivatives. (a) f ( x ) = x 2 + x + 1 (b) f ( x ) = x 4 + x + 1 x (c) f ( x ) = xe - x (d) f ( x ) = sin x cos x (e) f ( x ) = ln( 1 - x 2 ) (f) f ( x ) = ln(cos(2 x )) (g) f ( x ) = sin - 1 (cos x ) (h) f ( x ) = 2 3 x 2 (i) f ( x ) = e ln( x cos x ) (j) f ( x ) = x 2 1 - x (k)
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Unformatted text preview: f ( x ) = ( x 5 + 7 x + 1) 4 (3 x 2 + e 2 x + sin( 1 2 x )) 3 (l) f ( x ) = 2 sin 2 (2 x ) 3. For each of the following, nd the antidervatives. (a) f ( x ) = 1 x + 2 x + 1 (b) f ( x ) = sin x-cos x (c) f ( x ) = 2 e 2 x-1 x + x (d) y 00 ( x ) = x 3 + 4 x 5 , y (1) = 2 and y (0) = 1 (e) y = sec 2 x, y ( 4 ) = 1 4. Use the denition of the integral to show that: Z 2 1 3 x 2 + 2 x + 1 dx = 19 2 ....
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