MATH 140 Lecture : Notes Differentiation WITH THE ANSWERS

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: all

Document Summary

The rate of change in the values of f as x moves from a to a+h is f (a+h) f (a) h lim h 0. It is called the derivative of f at a and is denoted by f " (a) Thus f " (a)=lim h 0 f (a+h) f (a) h if the limit exists. Ex. f ( x)=x2 f " (a)=lim h 0 f (a+h) f (a) h. =lim h 0 (a+h)2 (a)2 h lim h 0 a2+2ah +h2 a2 h lim h 0 h(2a+h) h. Does f " (0) exist? f " (0)=lim h 0 f (0+h ) f (0 ) h. *at this point, we need to consider 1 sided limits h 0 ( 1)= 1 h 0 h =lim h 0 h h h =lim h 0 f (h ) Is f continuous at 0? h 0 x x =0 h 0 f (x)=lim lim h 0+ x2=0 h 0+ f (x)=lim lim f (0)=0.