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2. Show that p-1 E(+1) = 2a +(*)(4+1) k=0 l=0 Hint: Fix an 0 <I<p –...
2a) Let a, b e R with a < b and let g [a, bR be continuous. Show that g(x) cos(nx) dx→ 0 n →oo. as Hint: Let ε > 0, By uniform continuity of g, there exists δ > 0 such that 2(b - a Choose points a = xo < x1 < . . . < Xm such that Irh-1-2k| < δ. Then we may write rb g (z) cos(nx) dx = An + Bn where 7m (g(x)...
. Consider the density funetion noiudue 0 < x < I fix)=k/x. elscwhere. 15. Consider the density funetion 2ib'svitslumo 0 1 fix)k. C. elscwhere. (a) Evaluate k (b) Find F(x) and use it to evaluate P(0.3 < X < 0.6) 15O bro nsy bhs nsom
A chemical reaction, A+B → P, has the following mechanism: 2A< Ki>A, (fast to equilibrium) A+B&K, ™C (fast to equilibrium), A,+C-k>P+ 2A (slow) where Kį and K2 are the equilibrium constants for the first two reactions, respectively. k3 is the rate constant for the third reaction. (a) [5 points] Based on this mechanism, show that the rate of product (P) formation is: d[P] – k[A[B], where k is the rate constant of the overall reaction. Write k in terms of...
Let p be a prime. If for integers k and I we have rk = x (mod p) for all x E Z, (x,p) = 1 show that k =l (mod p – 1).
Consider the following pdf: ; 0<x<1 f(x)-2k ; l<x<2 0 otherwise (i)Determine the value of k. (ii) Find P(X 0.3) (iii) Find (0.1 〈 X 1.5).
For all n E N prove that 0 <e- > < 2 k!“ (n + 1)! k=0 Hint: Think about Taylor approximations of the function e".
p-1 mod 4, prove that Σ k ( )-0. Let p be an odd prıme. Suppose that p k=1 p-1 mod 4, prove that Σ k ( )-0. Let p be an odd prıme. Suppose that p k=1
29, [2] * Fix k, n є P. Show that n+k-1 a2k-1 where the sum ranges over all compositions (a,... , ak) of n into k parts. 29, [2] * Fix k, n є P. Show that n+k-1 a2k-1 where the sum ranges over all compositions (a,... , ak) of n into k parts.
Could I have help with entire question please. P+1 pt1 for any 2. In this question we will show by first principles that xpdz = p>0 a) Prove that (b) Use the formula (k +1)3- k3k23k +1 repeatedly to show that (for any n) m n (n+1) 7n and thus k2 mav be written in terms ofk- . Specifi- k-1 cally rL Note: An induction argument is not required here. (c) Using the same method with (complete) induction, or otherwise,...
Can someone show me how to do question 2a and all 3 and 4? I tried ratio test for 2a, but if x = 0, rhe proof doesn't work. Thanks a lot. 2. Prove the following. (a) The series o converges for all 3 € R. (b) For n e N and k € {2,..., n}, the binomial coefficient (7) satisfies *)-(-5) (-)-(---) (c) For x > 0, the sequence (1 + 5)" is monotone increasing and bounded above by...