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Which is different than the others? O Σ2, (-1)+1 η 4η Ο Σ ! Ο Σ1 η 5n2 -5.7 6n2 -6.7 =1
1. Show that, for every n > 1: n ka n(n + 1)(2n +1) 6 k=1
Show that for a material element subjected to principal stresses σ1, σ2 and σ3 (triaxial stress state), the shear stress that develops along the octahedral plane with direction cosines-,-,-in the system of axes 1, 2, 3 is given by
7.- True/False (a) If H0 : σ1-σ2, then F* < 1 for any two random samples. (b) For any random sample Fa/2,n-2 > χα,n-1 (d) If Ha : μ 140 then P Plt < It * l) (e) In any hypothesis test where the P 0.02 and α 0.02, the conclusion is to Reject Ho
H5. EXTRA CREDIT Assume that the numbers μ, r, σ1: σ2, T. T2, K, and So are given and that 0 < Ti < T2. The function σ(t) is defined as if t E [0, TI), ơı, What is the price of European call option with strike K whose underlying security has the price that satisfies S(t)-Soeμ1+σ(t)B(t), where B(t) is a standard Brownian motion? H5. EXTRA CREDIT Assume that the numbers μ, r, σ1: σ2, T. T2, K, and So...
6 Find a series solution, centered about Io = 0, for the given ODE (1 – 2?)y" – 2xy + 2y = 0 Extra Credit: Using only differentiation, integration, and the series formulas given on handout 6 on Canvas, find a closed form for the series found in question 6. You must show all work, algebra, and calculus involved in determining the closed form of the series to receive the extra credit. -14x<1 Sinx=Σ(-1-1 -1 1) 1-3 2) 3) (2n-1)!...
All i need is 3, 6, 7, 8 Use the ratio or root test to determine if the following series are convergent or divergent. If the ratio or the root test fails, indicate why. X 1 2n 1. Σ 5. Σ (2η)! n=1 n=1 n X 2n 2. Σ(3) 6. Σ (η)! n=1 n=2 n2 3. Σ 5 (η2 +1) 7. Σ 4η n=1 n=2 4. Σ (2n)! 8. Σ1 η! νη n=2
proof: Let be a k-form and η be a 1-form on Rn Let be a k-form and η be a 1-form on Rn
Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities σ1, σ2, σ3 and σ4 on their surfaces, as shown in the following figure (Figure 1) . These surface charge densities have the values σ1 = -7.50 μC/m2 , σ2=5.00μC/m2, σ3 = 1.30μC/m2 , and σ4=4.00μC/m2. Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets.What is the magnitude of the electric field at...
With the calculus of residues show that (2n)! cos2n 6 do = 1720 (91) 2 (2n – 1)!! -, =- " n= 0, 1, 2, ... (2n)!! Hint. cos 0 = (eie +e-10)/2 = (2+z-1)/2, 1z| = 1.