MATH100 Lecture Notes - Marginal Cost, List Of Trigonometric Identities, Quotient Rule

• School: University of Alberta
• Department: Mathematics
• Course: MATH100
• Professor: Ian Blokland

Document Summary

Part 1: the derivative as a rate of change (text: 3. 4) Recall the falling basketball d (t)=4. 9t2 vavg= d. Let s (t) represent the position of an object. Rate of change of s(t) : velocity v (t )=s"(t ) speed v (t) . Rate of change of velocity: acceleration a (t )=v"(t )=s" "(t ) s" "" (t )= j (t ) jerk s(4 ) (t) snap s(5 )(t )crackle s(6)(t ) pop. Example: jumping on a trampoline h(t)=7t 4. 9t2 v (t )=h" (t)=7 1 4. 9 (2t)=t 9. 8t. At top of the jump , v=0 0=7 9. 8t t= 5. All the objects rise/fall with constant downward acceleration (galileo) Example: c ( x)( cost ( of objects produced)) marginal cost c"( x) Part: 2 derivatives of trigonometric functions (text 3. 5) f ( x)=sinx f " ( x)=lim h 0 f ( x+h) f (x ) h d dx (sinx )=lim h 0 sin ( x+h) sin( x) h.