Q 4.68a) Find the values of the constants a, b, and c so that the directional derivative of Ф , 2. -1) has a maximum...
1. Find the directional derivative of the function f(x, y, z) = 2.cy – yz at the point (1,-1,1) in the direction of ū= (1,2,3). Is there a direction û in which f(x, y, z) has a directional derivative Dof = -3 at the point (1,-1,1)?
1 point) Let a and b be constants, and let Let f(t,) . Then f is a smooth function of variables t and z, and frz Let z-W be a Wiener process. The goal is apply Ito's lemma in the form, to find a stochastic differential equation that is satisfied by Y = f(t, z) After applying Ito's lemma, dt t dz Type z Wt as z. Since Y e is a common factor on the right side, after dividing...
Find dy/dx of the next relations Sol: y ylx 1 1-Cx C 2) 1+cx y' (1+cx1-cx a+bx ab 3) y= In Va-bx y's a2-b'x 4) y= atan (t); x = bcor (t) 6) x+2 7) y = 2v+ 45; donde v 52., W sec X 8)4x+3 8xy+e -e+ 8cos[tan(y)] = 0 arcsec (); x = elog2 (Int) 9) y 10) y sen[tan(x )] 11) y = cos[sen' (x)] cot + 4 12) y 13) y = [sec'(secx))P 14) y [Beae...
aw au B. Find the points in which the line x = 1 + 2t, y = -1 – t, z = 3t, meets the three coordinate planes. C. Evaluate and at the given point. w = In (x2 + y2+ z2), x = ue") y = ue'sinu, z = uecosu, (u, v) = (-2,0) A. Find the volume of the solid. II. z = 4 - 4(x2 + y2) z = (x2 + y2)2 - 1
Question 1 < Find the tangent plane to the equation z = 3.12 2y2 + 3y at the point (-4, -3, - 75) 2 Question 2 Find the tangent plane to the equation z = 5ex°-by at the point (12, 24, 5) Question 3 < > Find the tangent plane to the equation z = 5y cos(3x – 2y) at the point (2,3,15) z = Question 4 at the point (4,2,8), and use it to Find the linear approximation to...
Problem 5. (1 point) A Bernoulli differential equation is one of the form +P()y= Q()y" (*) Observe that, if n = 0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u =y- transforms the Bemoulli equation into the linear equation + (1 - x)P(3)u = (1 - x)^(x). Consider the initial value problem ry' +y = -3.xy?, y(1) = 2. (a) This differential equation can be written in the form (*) with P(1) =...
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0 1. Consider the Partial Differential Equation ot u(0,t) =...
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds- 1 point)...
(a) If var[X o2 for each Xi (i = 1,... ,n), find the variance of X = ( Xi)/n. (b) Let the continuous random variable Y have the moment generating function My (t) i. Show that the moment generating function of Z = aY b is e*My(at) for non-zero constants a and b ii. Use the result to write down the moment generating function of W 1- 2X if X Gamma(a, B) (a) If var[X o2 for each Xi (i...