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Chapter 1 Notes

by: Dkrefft

Chapter 1 Notes Math 1150

Marketplace > Tulane University > Math > Math 1150 > Chapter 1 Notes
GPA 4.0
Long Calculus I
Frank Tipler

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About this Document

Notes from Chapter One and the SI notes from 9/30 and 10/1. Sections 1.1-1.5
Long Calculus I
Frank Tipler
Class Notes
long calculus, frank tipler, long calc, Calc, tipler
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This 6 page Class Notes was uploaded by Dkrefft on Saturday October 3, 2015. The Class Notes belongs to Math 1150 at Tulane University taught by Frank Tipler in Summer 2015. Since its upload, it has received 108 views. For similar materials see Long Calculus I in Math at Tulane University.


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Date Created: 10/03/15
Math 1150 Long Calculus Notes 928 fx xn power function fx W root function 2 x 3x4 fx 3 rational function x 6x7 fx Sinx trig function fx exax exponential function fx lognx f x lnx log function 0 12 2 Name the type of function A y 7tquot exponential B y x power C y x22 x3 algebraic polynomial function D y tanT cosT trig function E y 55 rational function ratio of two polynomials F y algebraicfunction 0 12 10 Find the expression for the cubic function fx ax3 bx2 cx dgoing through the points 30 and 42 f3 0 a02 bO c fx ax2 bx f3 0 a32 b3 c 09a3bc c 9a3b f4 2 a42 b4 c 2 16a 4b c 2 16a4b 9a 3b 7ab2 0 Since this is a parabola we know that there is also point at 22 f2 2 a22 b2 c 2 4a 2b c 2 4a 2b 961 3b plug in C 2 5a b 27ab 4 2a0 solve a2 b2 722 14 12Sob 12 c 92 3 12 18 36 18 so c 18 The resulting equation is f x 2x2 12x 18 yfx cgt0 yfxc moves fx up or down by c 0 yfxc moves fx left or right fxc moves it to the left fxc moves it to the right 0 ycfx stretches fx by c Composition f 0 9XfgX f 0 g 0 h XfghX TVpe equation here 1434fx x3 2fg 1 4x 0 a compute fgx 1 4x3 2 0 b compose gfx 1 4x3 2 0 c compose ffx x3 23 2 x 1 2 3 4 5 6 FX 3 1 4 2 2 5 GX 6 3 2 1 2 3 930 Exponential functions fx 10quot 10 being a positive real base and x being the exponent 0 general case f x bxb gt 1 x integer fx 10quot 102 100 101 10 100 1 F1 906 19quot gO b0 1 o 104 W 10 104 laws of exponents 139 babc baC 2 b 1 ba 3 bac bac o 14 2 1 14 a 8 8 g 2305 2 16 b x3x23 x33x6 27x7xlx6 261 x7 0 14 20 find domain a gd 110t 102 10t 102 2 0 2 00 b gt sin et 1 e has to be a real number so oooo 0 14 22 fx Cbquot C constant and b constant C f 1Cb 13 3soC3b 4 4 f1 Cb1soCb i E 3 3 3 9 2 22 4 2 ac ac 2 32 b 323 50b b be 42 x Inverse Functions 15 P 3 definition of a given function fx its inverse function is written as f 1x and defined by f 1fx x you could also have ff 1x x fx will have an inverse only if fx is one to one when you get a unique value of y for every x and only one y the exception is f x x2 f x 19quot logarithmic function is the inverse of the exponential function 10gb bquot x natual log loge x lnx blong x laws of logs loga xy loga x loga y logag loga x loga y loga xT rloga xloga a 1 15 36 a logs logs 1 logs 125 log52 310g5 5 b lnei2 ln1 lne2 21ne 2 Session with Radhika 930 12 11 find the cubic function fX ax3 bx2 cx d 6 a13 b12 1c 6abc 0 ab c b 0 8a 4b 2c 0 24a2bc 04a2acc a cbac 06a3c0 1 ba 2a b cc ba d0 c2a 6 1 1 2C 2C C 2a 6 so a3 and c6 and b3 fx x3x2 3x 6 ylogexey xsoylnx ylog3x3yx lne 11n1 0 1 equot2 1 el x 14 19 Find the domain offx 1 el quot2 0 1 61 quot2 In 1 In 6139quot2 0 1 x2lne 0 1 x2 1 x2 x i1so the domain is 00 1U 11U1 oo 0 theoretical example ln3 1 x2lne ln3 1 x21 ln3 1 x2 ln3 1 x2 1 ln3 xquot2 1431fx x3 2x2gx 3x2 1 fgx f3x2 1 3x2 13 23x2 12 1 1 391 QUIZ 1 Find tlhe domain of m x25x6 4V2x 1 435 2X95 3 tZx 1 04 1 2 10 x 30x 2 1 x gt x at 2x at 3 1 domain E 2 U2 3U3 00 Session with Radhika 101 14 21 fx Cbxc and b are unknown 6 f1 Cb1 630b ECb 6 f3 Cb3 24 6 3 c 24 C 216 c1 2 72 24 3 C 216 24c2 24 24 9 c2c i3b i2 f x 132quot 0 14 31 The half life of bismuth 210 is 5 days a Sample mass is 200mg find the amount after 15 days fx Cbquot f0 200 Cb0 630 C 200 f5 100 Cb5 100 1oo 200195 0 zoo m 200 3 200 33 b The amount after t days 1 200 g 200 mg 1 1 5t ft 200 2 14 19 b f x 810 domain top 00 00 bottom 00 oo fxsinx domain oo oo fxcox domain oo oo 1 14 1b find dom4aln of 1 x23 IslH 1 96 963 102 class notes PPONT procedure p58 write yfx solve for x in terms of y interchange x and y set y to the inverse of fx 15 52 find the inverse function of f x 4x 1 2x3 4x1y2x3 2x2xy1 3y x42y13y 1 By x4 2y 13x y4 2y f 1x 13x 4 2x Inverse trig functions sin 1Sinx x arcsin Sinx cos 1cosx x cosarccosx How to restricta sin function to make it one to one f x sinxO E 5 5 2 2 0 15 66 Find the exact number 1 1 a 2 1 sin sin 1 Sine 9 1 9 sm SO 4 1 E b cos 2 6 9 cos 2 7T cos


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