3. Consider the functions, m(x) = x + 3x and p(x) = 2x + 5, Find m(p(1)) b. Find m(p(x)) a. c. Find p(m(1)) d. Find p(m(x)) 4. Consider the functions b(x) = (x – 1) and c(x) = Vx+ 1, b. Find b(c(x)) a. Find b(c(9)) d. Find c(b(x)) c. Find c(b(9))

Q: 1. Suppose f(-2) = 3, f'(-2) =-4 g(3) = 2, g'(3) = -1 1.1. What is the linear approximation to k(x)…

A: Linear approximation formula is k(x)=k(a)+k'(a)(x-a) Formula of derivative of composition of…

Q: 1 2) Find the linearization at x = a and use it to approximate f(b). f(x) = a = 6 b = 6.1 V4x+1 f(x)…

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Q: One of the critical points of f(x,y) = x³ – 5y² + 10y – 27x is:

A: The given function is fx,y=x3-5y2+10y-27x. The critical points of a function f(x, y) are obtained by…

Q: Find the quadratic function f(x) = ax + bx +c that goes through (2,0) and has a local minimum at (0,…

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Q: 3. Find the fixed point(s) of f : [1, 0) → [2, 0) defined by f(x) = vx² + x.

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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)…

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Q: 21) Find the maximum and/or minimum values of f (x, y) = x² + 2xy + 2y² - 6y + 2

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Q: 28. Find the critical points of f(x) = x3 – 3x2 - 3. а. (0,—3)аnd (2, -7) b. (0,3)and( 2,7) c. (0,2…

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Q: (c) Show that V(3) = o²(X'V-¹X)-¹.

A: 3. c From the given information, y=Xβ+ε Eε=0, Vε=σ2V From the part b, β^=X'V-1X-1X'V-1y

Q: Find values of C1 and C2 so that the given functions will satisfy the prescribed initial conditions…

A: A detailed solution is given below.

Q: 1. A) Find the linearization of the function at the given point. f (x, y) = 2 + x In (4 – xy), at…

A: (NOTE- These are two completely different questions, only required to do the first one. Please post…

Q: Max z = x1 + x2 s.t. 2x1 + x2 ≤ 20 x1 +3x2 ≤ 15 x2 ≤ 4 x1, x2 ≥ 0

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Q: 35. Give linearly independent functions that are annihilated by D² (D² – 2D + 10).

A: We will find roots for the equation and use concept of differential equations to find the linearly…

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

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Q: 4) Find the orthogonal trajectories of the family of the curves x² = 2y – 1+ ce¯2y.

A: We need to find the orthogonal trajectories of the family of the curve given by x2=2y-1+ce-2y We…

Q: 4. Find and classify the critical points of each of the function f(x,y) = x² + y² + 3xy.

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Q: The critical Points of f (x, y) = x³ – 3x + 3y² – 6y are:

A: The critical points of a function f(x, y) can be obtained by solving the partial derivatives ∂f∂x=0…

Q: The line tangent to y = ƒ1x2 at x = 3 is y = 4x - 10 and the line tangent to y = g1x2 at x = 5 is y…

A: The line tangent to y=fx at x=3 is y=4x-10 and the line tangent to y=gx at x=5 is y=6x-27. Consider,…

Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

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Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: 2. Find the equation of the linear function z = c+mx+ny whose graph contains the points (0,0, 0),…

A: We solve only one problem at a time so please submit them one by one for fast and thorough answers.

Q: X, t Xx t 2 Xz531 2X, + X> t Xz Z22 Naximzed By: 233y,tax2tdxg

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

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

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Q: 3- Suppose that s(x)dx 5. Find A- B- S V3 f(2)dz D-

A: Definite Integral of function f(x) in the interval of [1, 2] is 5. The function remains the same for…

Q: (1) If f(x) = { 3 x2 ; -1<x<2, then 0 ; otherwise compute [ xf (x) ]dx and [x²f(x)]dx

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Q: Find the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

Q: 9. Let f(x) = x³ – 3x² + 3. a. Find the y-intercept of the function; b. Find all critical points of…

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Q: 6. Consider the function f(1, y) = Suppose we would like to make small changes Ax and Ay to the two…

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Q: What is the particular eq. of the given:   y"-3y'+2y= xe^x +1

A: NOTE: Refresh your page if you can't see any equations. . for the homogeneous system, the auxiliary…

Q: 1 of f(z): is z2+2z+2 %3D

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Q: 3. Differentiate. a) M(u) = (1 – 4u²)(u+2) b) g(x) = (-x+3)(x – 10) c) p(n) = (5n+1)(-n²+ 3) d) A(r)…

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Q: If (a,ß) is a saddle point of the function f(x,y)=20y²-y³+3x2-6xy, then a+ß=

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Q: the differential equati x²y' – 2y = Inx² is cje2* + c2e¯* – x + 5 O c1x² + c2x=1 – In x + ; O 2 +…

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Q: 1. If (x and jy) = 3 + j8, find x and y.

A: Note:  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

A:

Q: 1) Show that (a) y =xe satisfies the eq. xy' (1-x)y (b) y =xe"A satisfies the eq. xy'=(1-x²)y

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Q: Suppose the function f(x)=3x^4+ax^3+bx^2 has a critical point at x=2, for which f(2)= −80. Determine…

A: Suppose the function f(x)=3x4+ax3+bx2 has a critical point at x=2, for whichf(2)= −80. Determine 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: 2. Verify the following derivatives : d а) dx 45x +(Vx + b) 4Vx(ax² + bx +c)]=,_ d 1 -(5ax² + 3bx +…

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Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

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Q: Consider a firm that produces a single output good Y with two input goods: labor (L) and capital…

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Q: Find the critical point of the function f(x,y) = 7x²y² + 4y² + 4x².

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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: Consider the minimization of the function f(w1, x2) = (x² + x2 – 11)² + (¤1 + æ; – 7)² with starting…

A: As per te question we have to use one iteration of Powell's method , to find the optimal solution to…

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

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Q: Find the linearization of the function at the given point f(x,y)=-10x+8y-9 at (-7,4). A.…

A: I have appended the formula used in the solution part

Q: If we use the secant method on fx) = x+x+3 with x2 and X-1 = 1, then X, is

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Q: 2 Find / U(x) + 4g(x)]dx if -5 2 2 | f(x)dx = 6 and / g(x)dx = -3. -5 -5 2 [f(x) + 4g(x)]dx = i %3|…

A: Given∫-52f(x)dx=6∫-52g(x)dx=-3

Q: 7 If f(x, y) = (3x³ + 2y² – 30)', then fy is - given by :

A: