Calculus 1000A/B Lecture 16: Calculus 1000 A -Lecture 16- Section 2.7-2.8

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Kiriushcheva

Document Summary

Calculus 1000a lecture 16 - section 2. 7/2. 8- introduction to derivatives. Let"s say that there are two points, p ((cid:1876)(cid:2869), (cid:1877)(cid:2869)) and q ((cid:1876)(cid:2870), (cid:1877)(cid:2870)), and q approaches p (cid:3051)(cid:3118) (cid:3051)(cid:3117)= (cid:1876) 0 lim(cid:3051)(cid:3118) (cid:3051)(cid:3117)(cid:3052)(cid:3118) (cid:3052)(cid:3117: (cid:1865)= (cid:1865)=lim(cid:3051) (cid:1858)(cid:4666)(cid:1876)(cid:4667) (cid:1858)(cid:4666)(cid:4667) (cid:1876) say that point (cid:858)a(cid:859) (a, f(a)) is fixed and point (cid:858)x(cid:859) (x, f(x)) can change. Definition: let (cid:858)h(cid:859) = x-a or x = a + h. then h 0 when x a. Therefore: (cid:1858) (cid:4666)(cid:4667)=lim (cid:2868)(cid:1858)(cid:4666)+ (cid:4667) (cid:1858)(cid:4666)(cid:4667: this definition is equivalent to the one above, however this definition is often preferable.