4.1.5. Let f(x,y) = (x² – y², 2xy). Show that Df(a,b) (h, k) = (2ah– 2bk, 2bh+ 2ak) for all (a, b) e R². (By the previous problem, you may work componen- twise.)

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" +…

A:

Q: 4. Modify the Euler method to obtain the approximate values of y(3) and y'(3) y" – y' + y = t, 2<t<…

A: Given that    y"-y'+y=t                        1⇒y"=y'-y+t we will solve this problem through MATLAB…

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

A: Given: Tn+2=12Tn+1+Tn for n≥0 T0=a T1=b To find: The limit of Tn as n→∞.

Q: Thm 3.8 : Assume the sama condittons as in Thm 3.7. The Robin's problem Lu=f, 24 +bx)u = g ond2 has…

A: As per the question we have to prove that the solution to the Robin's problem will be unique if b(x)…

Q: The domain of the funsfon f(x) te 9) E2,21, or equivalenfly,t243 C) [4,00, 0r )(00,4),or…

A: This question can be solved by applying the concept of existence of function at various points on…

Q: 5.76 In Exercise 5.8, we derived the fact that f (y1, y2) = { 4Y1.Y2, 0< yi < 1, 0 < y½ < 1,…

A: Given tha joint pdf of Y1 and Y2, such that: f(y1, y2) = 4y1 y2    ,   0&lt;y1&lt;1 , 0&lt;y2&lt;1…

Q: 25-let F(xs.2)=x-x22 @ Find VF 6 write the equution of tngent Plame to the at Paint (2,1,1). Find…

A: The given function is,  F(x,y,z)=x2y2-xz2 We have to find,  a) ∇F b) Equation of the tangent plane…

Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: If L(x)=mx+b is the linearization of f(x)=2x³ - x +3 at x-1, then m= Using L to approximate 2(1.01)…

A:

Q: Solve the Pollowing dellay diffenential on the in te vval [os 2J by the mpth-d of steps. (a) dx =…

A: I have gotten a unsolved integration in that problem so i write as it is

Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

A:

Q: Given: f(x, y, z) = y²³ In (x + 2) + ³x cash (yz) 9). Determine if the level curface of at k = 0…

A: The given function is: fx, y, z=y5lnx+z+3xcosh yz a) Determine the if the level curve at k=0 passes…

Q: az Suppose z is a function of r and y, and csc Vr² + yz = 2"e»in z_ Solve for dz and dy

A: Given: csc x2+yz=zyesin x To find ∂z∂x and ∂z∂y.

Q: For the function f(x, y) = (3x + 4x')(k'y² + 2y) where k is an unknown constant, if it is given that…

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

A:

Q: 10 a- Let X1, X2, ..,Xn~N(0,0) and T Find %3D X2 E (T),Var (T)

A:

Q: 6. Consider the function f(x, y) = cot ¹(1+x) — 2e¹+³y If x = s²-t² and y = 3t+tan(1-s), use the…

A: Let's evaluate given partial derivative.

Q: 2. Use the method of Lagrange multipliers to show that for x, y ≥ 0, we have z"+"> (²+)" 2

A: Introduction: For minimizing a multi-variable function under some certain constraint or constraints,…

Q: Find for following 1.y = (x + v3x)S

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

A:

Q: Suppose that the total cost of manufacturing x units of a metal straws is C(x) = 2x2 + 6x + 12.…

A: We will use linear approximation of a function  let y = f(x) is the function  to find local linear…

Q: 1 1 Select all the antiderivatives of f(x)=-+ %3D x² +1

A:

Q: 2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that…

A:

Q: Find solution of an equation X f(x) 1.0000 1 1.25 0.8000 1.50 0.6667 1.75 0.5714 2.0 0.5000 a. Using…

A:

Q: 11. If f(r) = rª and g(r) = r³, then f' (x) = 4x³ and gʻ(x) = 3x². The Chain Rule multiplies…

A:

Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

A:

Q: Q2// A :-Compute for the following at t=1 z= ze", z =t, y=t1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint &amp; z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

Q: If g(x)=- A B d- ſ ^ [e' − In(2t + 1) ]dt, find g*'(x) . dx -2 2 (2x + 1)² 4 et + (2x + 1)²…

A:

Q: 1 4. Determine the value of b and k such that f(x) = kyx – + In (x³) + bx has Vx an inflection point…

A:

Q: Suppose that T(0) = a and T(1) = b are some constants. Define the running pairwise average as, for n…

A: Given: Tn+2=12Tn+1+Tn for n≥0 T0=a T1=b To find: The limit of Tn as n→∞.

Q: 2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁…

A: Solution : x1=X1+X2(et-K)      …(1) x2=X2+X1(e-t-K)   …(2) x3=X3    …(3) Solving above equations,…

Q: Suppose there is no known formula for g(x), but we know that g(2) = -1 and d (z) = V2 +5 for all x.…

A:

Q: t²x"" +2tx" + x' +2022x 0 for t> 0. If their Wronskian satisfies W(2) = 20, then find W(t) for all t…

A:

Q: 26.Show that if p is differentiable and p(t) &gt; 0, then the Wronskian W(t) of two solutions of…

A: Given: [p(t) y′]′ + q(t) y = 0 W(t) = c/ p(t)

Q: 4.2) Suppose you wanted to find the absolute extrema of f(x, y) = ax² + bxy+cy? + dx + ey on the…

A: The given function is, fx,y=ax2+bxy+cy2+dx+ey We have one critical point on the rectangle,…

Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, find the relative error…

A:

Q: 8. DETAILS SCALCET9M 3.10.003. Find the linearization L(x) of the function at a. Rx) = Vx, a = 64…

A: given,

Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: Consider the following PDe U + 2ury - 3uyy = 0 .. (1) The general solution of eq(1) is u(x, y) = f(y…

A:

Q: Suppose that we don't have a formula for g(x) but we know that g(1) = -4 and g'(x) = V x2 + 15 for…

A: g(1)=-4, g'(x)=x2+15 Finding the value of g '(1) g '(1)=12+15=1+15=16=4

Q: If f(x) - g(x) = 1, then f and g have the same antiderivative. %3D O True False

A:

Q: Find the value of k that makes function continuous at z=4 |2z + 6 z> 4 5z – k z< 4 f(z) = ualuo…

A: Continuity.

Q: A clamped cubic spline for a function f on 0,3 is given by [1+ax² -2x', S(x) = . [1-2(x-1)+b(x-1)² +…

A:

Q: 4.1 Use the trapezoidal rule to find an approximate value for V1+x'dx with n = 4.

A:

Q: Suppose z = 2xy where x = t^2 + 1 and y = 3 - t. Use the chain rule to determine which of the…

A: In the given question the functions are given as z=2xy , x=t2+1 , y=3-t . The objective is to find…

Q: 1. Use the Gauss forward formula with xo = 2.0,h = 0.15, n = 7 to find an estimate for f(2.5) if %3D…

A: Given: fx=xlnx. x0=2.0, h=0.15, n=7.   We can solve this by using Gauss forward formula

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

A: