ws_4 - Mathematics for Engineers I

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Mathematics for Engineers I (Math103). .. student-intranet/faculties/math/ 2009 - Fall/math103 Class Work Sheet 4 1 . 1. Use the definition of the derivative to find f 0 ( x ): i) f ( x ) = x 3 ii) f ( x ) = x + 1 iii) f ( x ) = 1 x iv) f ( x ) = 1 x v) f ( x ) = cos x vi) f ( x ) = sinh x . 2. (i) Show that the function f ( x ) = 3 x is continuous but not differen- tiable at x = 0. (ii) Show that f ( x ) = x 2 + 1 if x 1 2 x if x > 1 is continuous and differen- tiable at x = 1. Sketch the graph of f ( x ). 3. Find the equation of the tangent line for: (i) f ( x ) = x + 1 at x = 3. (ii) f ( x ) = sin x at x = π 4 . 4. If the tangent line to y = f ( x ) at (4 , 3) passes through the point (0 , 2), find f (4) and f 0 (4). 5. Find the average rate of change of f ( x ) = 1 x , on [2 , 3] and the instan- taneous rate of change at x = 2. 6. Find the derivative of the following: y = (2 x 3 + 3)( x 4 - 2 x ) y = x ( x - 1) y = x - 1 x +1 y = x
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This note was uploaded on 01/08/2010 for the course MATH Math103 taught by Professor Dr.prof.mostafaamer during the Winter '09 term at German University in Cairo.

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ws_4 - Mathematics for Engineers I

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