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## CALCULUS I

by: Kennith Herman

20

0

4

# CALCULUS I MA 113

Kennith Herman
UK
GPA 3.54

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
4
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 4 page Class Notes was uploaded by Kennith Herman on Friday October 23, 2015. The Class Notes belongs to MA 113 at University of Kentucky taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/228157/ma-113-university-of-kentucky in Mathematics (M) at University of Kentucky.

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Date Created: 10/23/15
1 Lecture 8 The derivative as a function 11 Outline 0 De nition of the derivative as a function de nitions of differentiability o Differentiability implies continuity 0 Example Finding a derivative 0 Example Finding tangent lines 0 Examples Points where a function is not differentiable 12 The derivative De nition Given a function f7 we may de ne a new function f 7 which we call the derivative off by W hm M h e M 7 provided the limit exists An equivalent de nition that is sometimes useful is f hm 7 yam yi A function is di epentiable at x7 if f x exists Thus the domain of f is the set of values x so that f is differentiable at x A function is di erentiable on an interval I if f is differentiable for each x in I 13 Differentiability and continuity Theorem 1 ff is di epentiable at x then f is continuous at x 14 Examples Example Find the derivative of fx Example Let fx lx Find all values x where f x 4 Find all value x where f 96 4 Find all tangent lines to the graph of f which are parallel to the line y 74x Example Let fx 237 8 Show that f is not differentiable at 0 Eat ample Let fx Where is f continuous Where is f differentiable Eat ample Let fx Give the domain Show f is not differentiable at 0 January 317 2007 Calculus I MA 115 Calendar Spring 2002 Text Calculus third edition by James Stewart ISBN 0 534 21801 6 Calendar The calendar below gives the dates of exams and other important dates for the course The list of problems below provide a guide to students and instructors as to the material to be covered The problems marked by s are particularly interesting Wed 9 Jan Fri Mon 11 Jan 14 Jan Wed 16 Jan Fri 18 Jan Mon 21 Jan Wed 23 Jan Fri 25 Jan Mon 28 Jan Wed 30 Jan Fri 1 Feb Mon 4 Feb Tue 5 Feb Review and preview 177 82 2 3 5 7 9 11 13 15 17 19 21 23 25 2 11 The tangent and velocity problems 11 3 5 7 12 The limit of a function 12 1 3 5 9 11 13 15 17 19 23 25 27 28 29 13 Calculating limits using the limit laws 13 1 3 5 7 13 15 17 19 27 29 33 39 59 61 75 76 78 13 Continued 14 The rigorous de nition of a limit lightly Martin Luther King Jr holiday 15 Continuity 15 1 3 9 13 15 17 31 33 37 39 45 47 49 59 60 16 Tangents velocities and other rates of change 16 1 5 7 11 13 15 17 21 Derivatives 21 1 3 5 7 11 13 15 23 31 33 34 35 37 39 44 45 53 55 59 60 61 22 Di erentiation formulas 22 1 34 Learn to di erentiatel 37 41 43 45 47 49 55 57 63 71 74 76 Last day to drop Review Review First exam 730pm 930pm room TBA Wed 6 Feb Fri 8 Feb Mon 11 Feb 13 Feb 15 Feb 18 Feb Wed Fri Mon Wed 20 Feb Fri 22 Feb Mon 25 Feb Wed 27 Feb Fri 1 Mar Mon 4 Mar Tue 5 Mar 23 Rates of change in the natural and social sciences 23 1 3 5 7 9 11 13 Appendix D Trigonometry reView 1 3 5 7 9 11 29 31 33 35 37 43 45 47 49 53 8385 24 Derivatives of trigonometric functions 24 1 3 5 7 9 11 13 15 17 19 21 23 25 27 33 35 37 43 45 47 53 55 25 The chain rule 25 1 47 odds 49 51 67 69 71 72 73 Implicit di erentiation 26 1 3 5 7 9 11 21 23 25 31 35 41 43 45 27 Higher derivatives 27 1 3 5 7 23 25 27 29 3141 43 47 49 52 53 28 Related rates 28 1 3 5 7 9 11 13 15 23 2731 Related rates continued 29 Linear approximations 29 31 33 35 37 39 41 45 47 51 54 210 Newton s method 210 1 2 3 13 23 25 31 Review Review Second exam 730pm 930pm room TBA Wed 6 Mar 31 Maximum and minimum values 31 1 3 5 7 9 11 13 15 21 29 31 33 35 37 39 45 47 49 51 62 63 67 69 Fri 8 Mar 32 The mean value theorem 32 1 7 17 19 21 23 24 25 27 31 33 35 Last day to Withdraw 11715 Mar Spring break Mon 18 Mar 33 Monotonic functions and the rst derivative test 33 1 3 5 7 17 23 27 31 33 35 37 39 41 43 47 49 Wed 20 Mar 34 Concavity and points of inflection 34 1 3 5 7 9 13 17 21 23 25 27 31 32 35 39 40 Fri 22 Mar 35 Limits at in nity horizontal asymptotes 35 1 3 5 7 9 11 17 1921 23 33 4143 53 55 61 65 66 Mon 25 Mar 36 Curve sketching 36 1 3 5 11 13 31 35 Wed 27 Mar 38 Applied maximum and minimum problems 38 1 3 5 7 9 11 13 15 17 19 21 23 29 33 35 4344 Fri 29 Mar 38 continued Sun 31 Mar Sir Isaac Newton died 27 March 1727 Mon 1 Apr 310 Anti derivatives 310 1 3 5 7 15 17 19 21 23 2737 39 43 49 55 59 63 65 67 Wed 3 Apr 41 Sigma notation 41 1 3 11 13 19 21 23 37 39 41 47 53 Mathematical induction Appendix E 1 7 9 Fri 5 Apr Review Mon 8 Apr Review Tue 9 Apr Third exam 730pm 930pm room TBA Wed 10 Apr 42 Area 42 1 3 9 11 13 23 25 26 Fri 12 Apr 43 The de nite integral 43 1 3 15 16 17 23 25 27 31 33 35 39 41 45 47 55 57 59 Mon 15 Apr 44 The fundamental theorem of calculus 44 5 7 9 17 19 21 23 25 27 29 31 41 43 45 59 61 63 65 69 71 81 82 83abc 87 89 Wed 17 Apr 45 The substition rule 45 1 3 5 7 9 11 39 41 43 53 55 63 65 67 Fri 19 Apr 51 Areas between curves 51 1 5 7 9 13 15 17 19 25 2933 45 49 Mon 22 Apr 52 Volume 52 1 3 5 7 13 15 17 19 25 27 33 35 4749 51 52 6168 Wed 24 Apr Review Fri 26 Apr Review Mon 29 Apr Final exam 83071030pm room TBA

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