Compute: gcd(51, 42) Find a pair of integers x and y such that 51x + 42y = gcd(51, 42) (x, y) = ( %3D

Q: Find the linear least squares polynomial approximation to f(x) on the d. f(x)= e, [C

A: The solution is given below

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x3 - 2x + 3, a = 2

A: We find f(x) and f'(x) at x=2

Q: The linearization at a = 0 to v8 + 5x is A+ Bx. Compute A and B. A = B = ||

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Q: b) Minimize the function f(x) = 4x + x²– 7x + 14 by using the Golden search method, in the interval…

A: Given function: fx=4x3+x2-7x+14 The interval given is 0,1. So, a=0, b=1. Using Golden search method,…

Q: %3D 1. Find the critical points forf (x) = 3x +

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Q: Find two positive numbers x and y such that x+y=60 and xy^3 is maximum.

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Q: Find two nonnegative numbers x and y such that xy 56 and 7x + 2y is minimized. y =

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Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: Find the maximum and minimum vvalues of f(x,y)=x3+3xy2-3x2-3y2+4

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Q: Evaluate the integral using Partial Fraction Decomposition. to +7t5+15t* + 32t3 + 23t² + 25t - 3 dt…

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Q: Find the linearization at x = a. f(x) = 6x®, a = 1

A: Linearization L(x) of function f(x) at a is given as L(x) = f(a) + f'(a)(x-a)

Q: Show f(x) = e and g(x) = xe linearly independent by finding its Wronskian.

A: Given: fx=exgx=xex The formula to obtain the Wronskian is Wx=f(x)g(x)f'(x)g'(x), where f(x) and g(x)…

Q: Find the Wronskian of a given set {yı, y2} of solutions of 7. (1 x2)y"-2xy' (a 1)y0, _

A: Consider the given equation.

Q: (h) Write down the Lagrange's polynomial through (xo, fo). (x1,fi), (X2, f2). Hence express 3x² +x+1…

A: Hello. Since your question has multiple parts, we will solve the first  part for you. If you want…

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval…

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Q: The linearization at a = 0 to v4 + 4x is A + Bx. Compute A and B. A = B = %3D II

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Q: m: Consider ozyz. Find all the first order partial denvatio

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Q: fx) =x+x, aニー Lcx) = ? (メフフ %3D

A: Given that fx=x+1x,      a=−1

Q: Find the linearization L(x) at x = a. 1 f(x) = - x - a = 1 %3D -

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Q: Q2: Find the total energy of the signal: fcos*(«) -sts π (x) Sts. x(t) : 0.w. (-R2, 0) (x2,0)

A: We will integrate the function in the given range.

Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: Find the linearization L(æ) of y = (81+ 2æ²)-1/2 at a = 0. L(x) =|

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Q: (h) Write down the Lagrange's polynomial through (x), fo). (x1, f1), (x2, f2). Hence express 3x²…

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Q: A function f(x,y) is homogeneous of degree 7 in x and y if and only if, __________.

A: Given problem is solved below.

Q: Evaluate 1 dz 2ni (2² – 1) where y is the closed path indicated in the figure. Hint. Either use…

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Q: Find Positive nombers X$ Y Such that X+y = 78 and 24xy a is maximized

A: To find two positive numbers 'x' and 'y' such that,  x + y = 78     => y = 78 - x And such that…

Q: Use Lagrange multipliers to maximize the function x, y) subject to the constrai x.)-Say, Sy 20

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Q: Evaluate the integral using Partial Fraction Decomposition. t+ + 7t5 + 15t* + 32t³ + 23t² + 25t – 3…

A: Given,            ∫t6+7t5+15t4+32t3+23t2+25t-3t2+t+22t4+2t2+1To find: Evaluate the integral using…

Q: Evaluate the integral using Partial Fraction Decomposition. t3 + t2 – 5t + 15 dt t + 2t3 + 8t2 + 10t…

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Q: (a) FAEN102 students must attend t hours, where t ∈ [0, H], of lecturesand pass two quizzes to be in…

A: The number of students who attend between the time t1 and t2 is given by: ∫t1t220t2dt For the first…

Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: Find y2 using Reduction of Order xy" – 3xy' + 4y = 0 , %3D

A: Given differential equation x2y''−3xy'+4y=0....1 Given a solution y1=x2 We have to find the y2 We…

Q: 1. y = V(x2 + 2) – x (x² +2) - х

A: Topic = Derivatives As per guidelines, At a time only one question can be answered out of different…

Q: q Find a positive numbers x and y such that x²+y= 48 and their product P(xjy) = xy is maximized. %3D

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Q: Let x y, z be three non-negative integers such that x + y + z The maximum possible value of xyz + xy…

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Q: Find the linearization of ƒ(x) = 2/(1 - x) + saqrt(1 + x) - 3.1 at x = 0

A: Given,

Q: fx) =x+x, aニー %3D LCx) = ? %3D

A: Our objective is to find the linearization L(x) at x=a.

Q: g. S 2x2-3x-36 dx (2x-1)(x2+9) 11

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

Q: Find the Wronskian of y = 2x + 3, y2 = x² + 3x, and y, = 1 -1. Use the result to determine if the…

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: Q6) Use LU Decomposition method to solve the sy stem: 6x - y - 4z = 9.3 x + y – 3z = 1.9 x + 2y – z…

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Q: Let g(x,y) = x³ – 6x² – y* + 5. Find and classify the critical point(s) of g.

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Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

Q: Find the Wronskian for the set of functions.{1, x, x2, x3}

A: we have to find the wronskian for the set of functions. {1, x, x2, x3}