Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

Q: Find the general solution of the given differential equation. xdy + 5y = x³ = x dx goed y(x) = 8 X 6…

A: Solution :-

Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: first and second at point x=3 of the given function the value of its derivatives, a) Calculate…

A: Given a function: fx=2ex+cosx-5x2+7x (a) To find the first and second derivatives of the function…

Q: 6. Let T: P₂ → P₂ be the linear operator defined as T (p(x)) = p(3x), and let B = {1, x,x²} be the…

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Q: When the eigenvalues of a b 4- [88] A d are ₁ = 2 and 2₂ = 0, what are the possible values of a and…

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Q: 3. Let x² +16y² + 2², where g is some nonnegative function of one variable such that g(1) = 3. Let S…

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Q: S (x + 2)(x + 1)¹/4 dx

A: Solution:-

Q: Determine the determinant and inverse of the matrix. A = 3 8 -1 8-1 -4 5 -7 -7 -4

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Q: Show that Y=22.4sin(1.1x) is an eigenfunction of the operator (d²/dx²). What is the eigenvalue? O O…

A: Here we have given that Y=22.4sin1.1x is an eigen function of the operator d2dx2. So, we have,…

Q: Suppose A E M₂ (R) is not a multiple and consider the linear function L on M₂ (R) with the criterion…

A: It is given that,  A is a real matrix of order 2 such that A is not a multiple matrix and L be a…

Q: show that: V f(r) = f'(r)r r where: r = xi+yj+zk

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Q: If you plan to buy a car in 2 years and expect to need $2000 for a down-payment, how much should you…

A: Future value of ordinary annuity  FV=R1+in-1i Where 'R' is regular periodic deposit amount, 'i' is…

Q: Compare the monthly payment and total payment for the following pair of $180,000 loan options.…

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Q: 3. 2x-y x-2y

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Q: 4. Let R³ be equipped with the dot product and let B = {(1, 1, 1), (0,2,0), (2, 0, 1)}. B is a basis…

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Q: Suppose P, Q and R are statements. Complete the truth table for the statement (P⇒Q) or (P and (not…

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Q: Here's an incorrect theorem with an incorrect proof. Theorem: All people are the same age. Proof:…

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Q: Find the inverse Laplace transform of the function. where y(0) = 1, y(0) = 0 and y" + 4y = f(t).…

A: Sol:- Since f(t) function is defined in the range t≥4 , so it can also be written as 3H(t-4)(where…

Q: 1. Consider the curve C = C₁ UC₂, where C₁ is the line segment from (0, 1.1) to (1,1,0) and C₂ is…

A: Given Data: The given curve is C=C1∪C2, where C1 is the line segment from 0,1,1 to 1,1,0 and C2 is…

Q: Suppose A is a 5 x 5 matrix for which det(A) = -3. What is the value of det(2A)? det(2A) =

A: Sol:- Given :- Det(A) = -3 and Dimension of 5 * 5 Matrix

Q: Classify the quadric surface. 2 x² + y² + z² = 1 4 ellipsoid hyperboloid of two sheets. hyperbolic…

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Q: Find a basis for the a.) column space and b.)null space for the matrix A below. Then provide the…

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Q: At which minimum Type value does the function g(x) = 3x² - 4x³ attain a - is the minimum value? and…

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Q: 1. y" + y = 0, y' (0) = 0, y' (n) = 0

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Q: Show ▼(E) - G&F - FVG G² G=0

A: Given : G≠0 To Show  : ∇FG =G∇F-F∇GG2

Q: . Please submit higher quality image or rewrite if its correct i cant read this.

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Q: a) Explain what it means, by definition, that a polynomial m(r) € P(R) is the minimal poly- nomial…

A: Given That : minimal polynomial for a matrix A∈ Mn×n(R) We have to explain  that the polynomial…

Q: a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. matrix A for…

A: For an n×n matrix A, a number λ is an eigenvalue if there exists a non-zero vector x such that we…

Q: Check if set X is linearly i ndependent, spans r3 and check for basis of r3 X={(1,0,0),(0,1,0),…

A: A set is a BASIS if it linearly independent and spans the vector space

Q: Translate the logic statement to an English sentence. Vx [M(x) A P(x)] Where M(x) = x is a musician…

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Q: + V -3 -12 Period: W Submit Question -+ -3- -5 1 A A Based on the graph above, determine the period…

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Q: Use reduction to triangular form to evaluate the determinant of the given matrix. 1 A = 3 16 24 0-1…

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Q: Question 8 Answer the following. Do the best you can entering in mathematical statements into the…

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Q: Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all t…

A: We know that the heat conduction equation is α2uxx=ut Given α2=1 So, the equation becomes uxx=ut…

Q: Solve the following dynamics equation using the Laplace transform with the initial conditions x(0) =…

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Q: Solve the given differential equation. All solutions should be found. 3 3x² - 9y - y³ 9x + 3xy² dy…

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Q: The figure to the right shows the letter L in a rectangular coordinate system. The figure can be…

A: We need to addition operation of matrix to move L .

Q: Consider the function D: P₂ → P2 given by D(ax² + bx + c) = 2ax + b. (a) Why did I call this…

A: It is given that,  D : P2 → P2  defined by  D(ax2+bx+c) = 2ax+b Then, we have to answer the…

Q: ACTURE QUISION, IS DESCRIBED BY THE EQUATION y = COSH x WHERE X e Y ARE HORIZONTAL AND VERTICAL…

A: (i)  y=cosh(104/60)=  2.9181

Q: Use a Taylor series centered at r= 1 to approximate the value of the integral farctan(x) dx accurate…

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Q: Let o be the 0= permutation 1 2 3 4 5 5 14 9 10 2 12 6 5 11 15 3 a) b) defined by: 6 7 6789 10 11 12…

A: Firstly change sigma in disjoint cycles and use the property to change cycle to transpositions.…

Q: II. dy dx 2x² x(y² + 1)

A: We have to find the best way to solve the given First Order Differential Equation by Finding…

Q: Consider the NxN-dimensional matrices A and B, where B=S¹AS (with S an NXN-dimensional non- singular…

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Q: Solve the given initial value problem. = 2 x²y² + xy³ x²y² + y² = 3 xy² + xy³ | xy² − y³ = 1 x²y² -…

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Q: 21 _) P') pludx= чи (и+1) сеn+ л 2 и+31 и+1

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Q: True of false If one of the eigenvalues of a matrix has a multiplicity of 2, then two eigenvectors…

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Q: At which value does the function g(x)= 3x^4 - 4x^3 attain a minimum and what is the minimum value?…

A: Sol:- Suppose that x=c is a critical point of fx then, If f 'x<0 to the left of x=c and f 'x>…

Q: 0)2= (?????) 16 (??? ???)2=(?????) 16 (?? ??) 10 (?????)₂ = (???

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Q: The market for a particular product is characterised by the following demand and supply functions:…

A: Sol:- At equilibrium price :- Qd = Qs 25-3P+0.2P2=-5+3P-0.01P221P2-600P+3000=0P1, 2=--600±-6002-4·…

Q: Consider the following function. T: R² R³, T(x, y) = (√x, 3xy, √y) Find the following images for…

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