MATH 1A Final: MATH 1A Harvard 1a Final 1997 Fall
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T t h 1 1 : 3 0. Q r t l f , o * No partial credit a n s w e r s . can be given for unsubstantiated. D i f f e r e n t i a t e t h e f u n c t i o n f ( x ) : * l n ( x ) . Iim x 2 e f ( x ) - f ( a ) x a. I i r n x-"> q" f ( x ) - f ( a ) x lirn l"+ o f(x+2h) - f(x) Note that the origin is not a point on this curve. T h e a ) c a l c u l a t e t h e v a l u e f ( 0 ) :
