QUESTION 11 Find the solution of x' + 2x' +x=f(t), x(0)=1, x'(o=0, where f(t) = 1 if t< 2; and f(t) = 0 if t> 2.
Let T(1, 0) – (1, 0) and T(0, 1) – (0, 2). (a) Determine T(x, y) for any (x, y). (b) Give a geometric description of T. o vertical sheer O vertical contraction vertical expansion horizontal expansion horizontal sheer horizontal contraction
QUESTION 9 Solve the following differential equation for x(t). x'(t) + X(t) = 0 x(O) = 2 Note: x'(t) is a time derivative of X(t). tis a time variable. x(0) is an initial condition of X(t). Ox(t) = expl-t) x(t) = exp(t) Ox(t) = 2*exp(t) Ox(t) - 2 exp(-1)
O Solve the initial value problem x" + 4x = (t - 1); x(0) = 2, x'(0) = 0
츨…<L. t-o(see (1) in Section i2 4) s bject to the given conditions. Solve the wave equation, .a a r u(0, t)=0, u(T, t)=0, t> 0 ux, o) 0.01 sin(5tx), 0u t=0 u(x, t) = n=1 Need Help? LRead it . Talk to a Tutor l
츨… 0 ux, o) 0.01 sin(5tx), 0u t=0 u(x, t) = n=1 Need Help? LRead it . Talk to a Tutor l
Please show all work.
3. x"(t) - y'(t) = -2t x'(t) + y"(t) = 0 x(O) = 0; y(0)=0; x'0) = 0; y'(0) = 0
Solve the initial value problem with 4 x'(t) = A, fort > O with x(0) = Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described Ax=b. Find the directions of greatest attraction and/or repulsion. x(o)= [1] A-[18 -16] -2 - 4 10 -16 2 -120 1 a. x(t)= (0,0) is a saddle point 5 2 120 b. x(t)= 1 + 6 le -61 (0,0) is an attractor 5 C. x(t)= o[1]...
17 Let X have the density f(x;0) = (0/2)*l(1 - 0)'-\*\14-1, 0, 1)(x), O SOS1. Define t(x)=21(1)(x). (a) Is X a sufficient statistic? A complete statistic? (6) Is X| a sufficient statistic? A complete statistic? (c) What is a maximum-likelihood estimator of O? (d) Is T= t(X) an unbiased estimator of 0?
linear algebra
Let T(1,0) = (4,0) and T(0, 1) = (0, 1). (a) Determine T(x, y) for any (x, y). (b) Give a geometric description of T. O horizontal sheer vertical contraction O vertical expansion horizontal expansion O vertical sheer O horizontal contraction
Determine e At by first finding a fundamental matrix X(t) for x' = Ax and then using the formula eAt = X(t)X(0)1. 0 2 2 2 0 2 2 2 0 First, find X(t). Choose the correct answer below 4t -2t 4t e -2t (1+t) e e -2t OA. X(t) (1+t)e4t 0 e2t B. X(t)= e4t 0 -2t -2t 2t - e - 2t (1t)e 4t e e 4t e 4t - sint sin t 0 (1t)e -2t O C....