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by: Cameron Brinkmeyer

WeekOneCalculus1914.pdf MATH 1914 010

Marketplace > University of Oklahoma > Math > MATH 1914 010 > WeekOneCalculus1914 pdf
Cameron Brinkmeyer
Differential and Integral Calculus I
Dr. Albert

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About this Document

This is week one of Calculus 1914. It focuses on limits.
Differential and Integral Calculus I
Dr. Albert
Class Notes
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This 4 page Class Notes was uploaded by Cameron Brinkmeyer on Saturday August 29, 2015. The Class Notes belongs to MATH 1914 010 at University of Oklahoma taught by Dr. Albert in Fall 2015. Since its upload, it has received 13 views. For similar materials see Differential and Integral Calculus I in Math at University of Oklahoma.


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Date Created: 08/29/15
Approximating limits Mathematician worries 0 Maybe it s really headed towards another number 0 headed towards nothing 0 What about intervals ending in 6 NewtonLeibniz o If Dt is nice then these worries are not a problem 0 We need to understand what a nice function is If FX gives something you care about as a function of something else you care about You can consider fiwlms H Say fx profitLifjhe se11 X iPhones 3 WNW If fx is a function then if 10ka a lg Heads to some number as h gets very small then we call that number the derivative of fx at X Def Given a function 1C iquot which is defined near xa We write lain L X a 01 Pronunciation The limit of fx as x approaches a is L o If there is a number L such that the outputs of the function can be made arbitrarily close to L by choosing inputs sufficiently close to xa x3 a 1 As x goes to 2 the function equals 7 o This does not mean that at 2 the function equals 7 o It could equal anything such as 80 or 0 o The function could also be undefined at 2 o It is what F2 should be based on the number very close to x2 Examples in F0053 liqttx l if grin T b0 GM W WE 39 x vv i M F gt0 3 The reason why the limit does not exist on some of the answers are A The limit approaches a point which is a break in the graph B The limit approaches an asymptote What if a function is given by a table or function Ex art Em K 0 k 37 We are still just guessing at the limit based on tables Now we want to be exact We want to calculate W n d 43 VaO a 7 h x We start with algebra we need to get rid of the h in the denominator W Eggs lo ll and an WA llm BM Xy0 The only thing that really changed is that the input of 0 Will no longer give us What the original function gave us This is the point of the limit 0 cannot be entered into the original or it Will be unde ned Therefore we do algebra to nd What the limit is by removing the restricting h in the denominator This does not mean that FX 13 but that the limit as X approaches 0 of FX 13 Conclusion 0 When taking approximations from a table the limit is never certain o limits may not exist 0 limits do not define a point but instead a limit defines what a point could be as it is approached from either side


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