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# Calculus I MATH 131

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This 3 page Class Notes was uploaded by Claudie Wintheiser on Monday October 5, 2015. The Class Notes belongs to MATH 131 at Christian Brothers University taught by John Peacher-Ryan in Fall. Since its upload, it has received 8 views. For similar materials see /class/219433/math-131-christian-brothers-university in Mathematics (M) at Christian Brothers University.

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Date Created: 10/05/15

Math 131 Fall 2008 Simple Derivative Rules Rule Name Function Derivative Constant Rule y b y39 0 Linear Function Rule y aX b y39 a Power Rule y X where n is any real y39 n X 1 number for those values ofX for which both X and nX 1 are de ned Exponential Rule y bx where b gt o y39 b Inb Natural Exponential Rule y 2 9X y39 eX 39 1 Natural Logan39thm Rule y InX where X gt 0 y Constant Multiplier RUe y kfX where k is a constant y39 kf39X Sum Rule y fX gX y39 f X 939X Use the Simple Derivative Rules to nd derivatives of the following functions 1 2 20 21 22 y 25x4 57x 121 yX 3 y 5X314 y39 5 4 fX X314 E y 9 fX 457 f X 0 y 4X2 8X d y25X2 3 5x 1 2 7 y 5X 3X19 y 25x10 y 3X 8 y3910X357 y3 1 5X 2 X 395 i y F y 3 y2 1 39 3 100 fX 7 7 3 6 78 y2X 7 y3914X 21X y 23ex y3e 5eX 2 3 2 y 23ex y39 23ex X2 y1 X25e3 y39 2X y5 we 23 24 25 26 27 28 29 30 3 x 3 l 33 34 3 36 37 38 39 01 y3XX3 y393n33X2 y 201X5 47X3 7X 6 4 x y 2X F 7e y 20 x y 12X5 F 7e 1 y6 2X 7 f2 X 2X 1 i y X y Xz ynX 4I I y nx y X gX 3X5 2nX 5 y 3ex nX dydX 3ex X 1 hX 15525 h39X 15525 In 525 3 yEX 2nxn4 y 1500 1j12X Since y 150010212X 1500126824 y39 1500 n126824126824x y 100001j6x y 532e 93 3 hX 2X3 14X 6 5 9X23 39 6X 13 7 y y 31 y1 2X9 5 Math 131 Fall 2008 Using the TI 89 to nd Riemann Sums for Use with Text Sections 43 and 44 17 If the function f is continuous on the interval ab the de nite integral I f xdx may be approximated by the righthand Riemann Sum 2 f x1 Ax or the lefthand Riemann 11 b a Your text tends Sum quot1 f x1 Ax where n is the number of subintervals and Ax to useihe righthand sum in section 43 As an example to evaluate this part of the righthand sum Zn f q on the TI 89 go to and select so that the command line is1 me z391n Ax We multiply the sum by Ax in order to obtain the righthand sum Exam le Set MODE to APPROXIMATE 4 To approximate Iv1 x3 dx with a righthand sum with n100 subintervals note that Z Ax ba E 02 andthat x1 aiAx 2L So the righthand sum n 100 50 approximation may be obtained by the command line ZJ12i50A3i110002 which gives If your calculator stays busy try either 1 putting in decimal points after all numbers or 2 setting MODE to APPROXIMATE

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