the solution please. thank you 4.5. Let di.....dx } be directions of unboundedness for the constraints...
Real analysis. Please solve all questions thank you 1. Let h be a positive real number, a <c< d < b and let Sh c< x <d, J() = 1 0 r < c, x > d (a) Using the definition only, find ſº f(x)dx. In fact, given e > 0, you should find an explicit d > 0) which works in the definition. (b) For a given partition P of [a, b], find a good upper bound on S(P)...
please prove part (b) use complex analysis and calculus of residue -dx neif a> 0 5. (a) x2+1 (b) For any real number a > 0, cos x dx ne"/a. a Hint: This is the real part of the integral obtained by replacing cos x by e
Please explain every step! And please write clearly. Thank you! Let V be a the shape described by the following criteria in cylindrical coordinates: 0 < z <r, Find the average square of the distance from the origin of V.
all three questions please. thank you Prove that for all n N, O <In < 1. Prove by induction that for all n EN, ER EQ. Prove that in} is convergent and find its limit l. The goal of this exercise is to prove that [0, 1] nQ is not closed. Let In} be a recursive sequence defined by In+1 = -) for n > 1, and x = 1. Prove that for all ne N, 0 <In < 1....
help please and thank you 212 24" 4. Find a formula for II (1-5) and then p 4. Find a formula fo and then prove it by induction for all integers n > 2.
Let n ez, n > 0; let do, d1,..., dn, Co,..., En be integers in the range {0, 1, 2, 3,4}. Prove: If 5*dx = 5* ex k=0 k=0 then ek = =dfor k = 0,1,...,n.
show by steps, definitions and theorems " f(x) dx = 0 for all integers Let f(x) be a continuous function on (a,0). If n> 0, then show that f(x) = 0 on [a, b].
Let n > 1, and let S = {1, 2, 3}" (the cartesian product of {1,2,3} n times). (a) What is Sl? Give a brief explanation. (b) For 0 <k <n, let T be the set of all elements of S with exactly k occurrences of 3's. Determine |Tx I, and prove it using a bijection. In your solution, you need to define a set Ax that involves subsets and/or cartesian products with known cardinalities. Then clearly define your bijection...
Please solve all three. Thank you very much 5. (a) Let a be a constant (we can write “a ER” to mean “a is a real number”). Verify that y(x) = ci cos(ax) + C2 sin(ax) is a solution for y" = -a’y, where C1,C2 ER. (b) Consider the hyperbolic trigonometric functions defined by cosh(x) = et tex 2 ex – e- sinh(x) = * d Show that I cosh(x) = sinh(x) and sinh(x) = cosh(x). (e) Verify that y(x)...
#3.3.19 If anyone can start this, I’d appreciate it thank you! 3.3.18. Let X and Y be random variables, and let Y=aX+b constants. Show that (a) pxy=1 if a > 0, and (b) pxy 3.3.19. If lpxyl=1, then prove that P(Y=aX+b)=1. 3.3.18. Let X and Y be random variables, and let Y=aX+b constants. Show that (a) pxy=1 if a > 0, and (b) pxy 3.3.19. If lpxyl=1, then prove that P(Y=aX+b)=1.