4. Let γ be a path with parametrization γ(1)-(1 12,1) where 2 1 £1. Compute lyidz. (Here 1/2 is understood by using pri...
Complex Analysis
1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r and 2, find the principal value of that integral, if it exists.
1. Let γ is a positively oriented circle centered at the origin with radius r r > 0 ecos(e2) +21)9 (a) For r £ {1,2}, compute the integral .Дег+1)(2+2)3 d (b) For r...
need help problem 2.1 2.2
affine mapping 1 1.2 Let K=[0, 1. The parametrization (or embedding) is given such that 1 uE K uER Line integral 1.3 Problem 2. 1. Let F Compute det(FTF), 2. Compute the length t of the line segment a(K) using the line integral formula.
affine mapping 1 1.2 Let K=[0, 1. The parametrization (or embedding) is given such that 1 uE K uER Line integral 1.3 Problem 2. 1. Let F Compute det(FTF), 2. Compute...
Let Log(2) be the principal branch of the logarithm. Then lim (Log(iy – 1) – Log(-iy – 1)) 40+ equals: 0-27 0-27i 0 0 27 O2ni None of these.
5. Let f(x) = e-} Log(z) (that is, f is the principal branch of z-1/2). Compute [flade, where (a) (2 points) y is the upper half of the unit circle C(0) from +1 to -1; (b) (2 points) y is the lower half of the unit circle C1(0) from +1 to -1.
(sin(π/z) -1dd 2. Compute the integral: sin(π/s)-.--d γ is the cl γ is the curve shown in the 2. where 721-1 following figure: arked points on the coordinate axes correspond to T,-T, 2, 2.
(sin(π/z) -1dd 2. Compute the integral: sin(π/s)-.--d γ is the cl γ is the curve shown in the 2. where 721-1 following figure: arked points on the coordinate axes correspond to T,-T, 2, 2.
4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e))
4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e))
4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e))
4. Evaluate the following integrals: f, where contour γ is a circle of radius 2 centered at the origin. z.İ f, -1-i,1-i,1+i,and-1+i. (z-0.1-1); where contour γ is the square with the four vertices ill) Jo (2+7 cos(e))
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3), 0StS 4 Evaluate F. dr Justify your answer. iii. Find a function y: R3-+ R such that F iv. Evaluate F.dr where「is the path y =r', z = 0, from (0.0.0) to (2.8.0) followed by the line segment from (2,8,0) to (1,1,2) 22 marks)
2. (a) Let i. Show that F is cnservative in R i. Let C denote the path 1+cost,2+sint,3),...
3. Evaluate the following payoffs for the game pictured here: (a) ui(οι, Γ) for σ,-(ja, 1/4, 1/4, 1/4) (b) 112(oi, О) for σ,-(1/8, î/4, 1/43/8) 2 OA | 2,2 | 2,2 2,2 2, IA 4,2 1,3 IB 3,4 1,3
Let X1,X2 be two independent
exponential random variables with λ=1, compute the
P(X1+X2<t) using the joint density function. And let Z be gamma
random variable with parameters (2,1). Compute the probability that
P(Z < t). And what you can find by comparing P(X1+X2<t) and
P(Z < t)? And compare P(X1+X2+X3<t) Xi iid
(independent and identically distributed) ~Exp(1) and P(Z < t)
Z~Gamma(3,1) (You don’t have to compute)
(Hint: You can use the fact that Γ(2)=1,
Γ(3)=2)
Problem 2[10 points] Let...