ECON 401: MATHEMATICAL METHODS IN ECONOMICS
FALL 2016
MARK MOORE
ADDITIONAL PROBLEMS
n ( n +1)
for n 1.
2
1.
Prove by mathematical induction that 1+ 2 + 3 + .+ n =
2.
Determine under what sets(s) of parameter restrictions, if any, each of the following
sy
ECON 401: MATHEMATICAL METHODS IN ECONOMICS
FALL 2016
MARK MOORE
SUPPLEMENTAL LECTURE NOTES FOR CHAPTERS 6 AND 7 OF THE TEXT
GENERAL NOTES: For most of the course, and in all practical applications, we will consider only realvalued functions. But
A. TM TT L THUYT
1.1. Khi nim cc tr hm s:
Gi s hm s ff xc nh trn tp hp D(DR)D(DR) v x0Dx0D
a) x0x0 c gi l mt im cc i ca hm s ff nu tn ti mt khong (a;b)(a;b) cha im x0x0 sao
cho (a;b)D(a;b)D v f(x)<f(x0)f(x)<f(x0) vi mi x(a;b)cfw_x0x(a;b)cfw_x0. Khi f(x0)f
khai trin taylor maclaurin (taylor expansion)
Shortlink: http:/wp.me/P8gtr-R
Ch dn lch s
1. Cng thc khai trin:
Gi thit hm s y = f(x) c tt c cc o hm n cp n + 1 (k c o hm cp n + 1)
trong mt khong no cha im x = a.
Hy xc nh mt a thc
bc n m gi tr ca n ti x = a