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assignment 4-1 using the definition of the derivative determine the derivative of the function fx radic2x 1 at x 12
assignment 3-1 suppose fx 1 - radicxcos1x for x ne 0 if f0 1 is f continuous at x 0 explain2 a prove there is some
assignment 2-1 let n ge 1 be a positive integer prove13 23 middot middot middot n3 n2n 1242 prove that for any
assignment 1-1 prove that the set of rational numbersx isin q x3 lt 2is a real number this is what we would identify
putnam tng - number theory1 do there exist 1000000 consecutive integers each of which contains a repeated prime factor2
putnam tng - functional equations amp iteration1 let f r2 rarr r be a function such that fx y fy z fz x 0 for all
putnam tng - limits amp estimation1 evaluate limxrarrinfin1xax - 1a - 11x where a gt 12 let n be a positive integer
putnam tng - chequer amp chess boards1 for each positive integer n let sn denote the total number of squares in an
putnam tng - polynomials and binomials1 define polynomials fnx for n ge 0 by f0x 1 fn0 0 for n ge 1 and ddxfn1x n
putnam tng - evaluation of integrals1 a evaluate the integralsin 0intpi sinnxsinx dx and nbspjn 0intpisinnxsinx2 dx
putnam tng - sequences and convergence1 let d be a real number for each integer m ge 0 define a sequence amj j 0 1 2
putnam tng - polynomials1 find polynomials fx gx and hx if they exist such that for all x2 let k be a fixed positive
1 let f be a real-valued function on the plane such that for every square abcd in the plane fa fb fc fd 0 does it
1 find with proof the largest number which is the product of positive integers whose sum is 20132 what arrangement of
1 suppose x y 1 and xy -1a find x2 y2b find x3 y3c find x10 y102 a let s be the set of all numbers in the
1 express cos3theta in terms of cos theta2 the polynomial fx x4 ax3 bx2 cx d has real coefficients and f2i f2 i
1 let s be any arc of the unit circle lying entirely in the first quadrant let a be the area of the region lying below
1 place a knight on each square of a 7x7 chessboard is it possible for each knight to simultaneously make a legal move2
1 let rp 1111 middot middot middot 11 be the positive integer with p digits all of them 1 for which p is rp divisible
1 determine all polynomials x2 px q with roots x p and x q2 a consider the quadratic polynomial qx x2 ax b find
1 a what are the last two digits of 32014b what are the last two digits of 9720032 a prove that this sequence contains
1 show that in any finite gathering of people there are at least two people who know the same number of people at the
1 you have 95 factors to test each at two levels each run costs 5000 in labor and materials each factor dropped saves
1 a markov chain with three states s123 has the following transition matrixadraw the state transition diagram for this
write an equation for the polynomial graphed below12345-1-2-3-4-512345-1-2-3-4-5 find a degree 33 polynomial that has