1. Parametrize the curve-segment C(t) of the parabola y = x² from (1, 1) to (2,4) then find [x² dx + y²dy. с

Q: Let X = C[0, 1] be a metric space with metric d(f,g) max {f(x) = g(x)}. x[0,1] Prove that the…

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Q: Find the derivative of the function. esin r In(1+2v)dv CoS z

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Q: If a and bare nilpotent elements of a commutative ring, show that a + b is also nilpotent. Give an…

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Q: D E B F Find an Euler path for the graph. Enter your response as a sequence of vertices in the order…

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Q: Numerical Methods. Using h = 0.2, approximate the value of y (3) for the given differential equation…

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Q: Suppose you plan to have $30,000 in 10 years from now and you can invest your savings at 2%…

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Q: Producers' Surplus The manufacturer of a brand of mattresses will make x hundred units available in…

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Q: 19. Evaluate 2 2+x2+x+y SS S f(x,y,z) dzdydx where f(x,y,z)=4. 0 0 0 Answer: 112

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Q: For the matrix below: [1] [2] [3] [1.] 3 4 7 [2.] 6 8 2 [3.] 4 3 9 What is A[-c(1.3).]? Choose one…

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Q: 2. A graph G has 9 vertices. Three have degree 4, two have degree 2, two have degree 1, and two have…

A: We use Handshaking Lemma for a Graph.

Q: The left end of a rod of length I is held at temperature 0, and the right end is insulated. The…

A: Given: A rod of length L such that: Temperature at left end is 0 Right end is insulted. Initial…

Q: In game theory, the strategy that has a higher payoff than any other strategy—no matter what the…

A: Answer In game theory, Superior strategy: states a situation where one player has a superior tactic…

Q: [n^2cos(n/2)] / 2n^2 +1 does this sequence converge or diverge & w

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Q: a) f(x) = -e (x+1)-1 x y = 2-x Transformation: Domain: b) f(x) = sin ¹(x + 1) + 1/2 P = x=y= sinx…

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Q: Find a linear approximation in order to approximate the change in f(x, y, z) = e4x cos(5yz) when…

A: Given f(x, y, z)  = e4x cos(5yz)  When moving from the origin a distance of 0.3 units in a direction…

Q: f(x, y) = -8x²-7y² + 6x + 4y

A: In that given function we have to find gradient and comparing with the given gradient we have to…

Q: Using the given graph, approximate the area under the curve from x = 3 to x = 6 using 3 subdivisions…

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Q: f (x) = 6x6 + 13x5 + 3x4 − 2x3 − 30x2 − 56x − 24. (a) Use the Rational Zeros/Roots Test to list all…

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Q: 22. Evaluate the volume integral for scalar function f=x² + y² +z and V is a closed region bounded…

A: The given problem is to evaluate the given volume integral of the given function f=x2+y2+z over the…

Q: Prove that the inner derivations ad x, x∈g are an ideal on Der(g)

A: Prove that : The inner derivative adx , x∈g are an ideal on Der(g).

Q: 28. [ TT/3 TT/6 2 csco csc o 2TT 0 p² sin o de dp do

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Q: The acceleration of a particle moving along a horizontal line at t seconds is modelled by the…

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Q: Sketch the level curve z = k of z= =(x² + y²) for k=0, 2, 4, 6, 8. Choose the graph of all level…

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Q: termine the general/particular solution (whichever applies): + 4y' + 4y =(3+x) e -2, when x = 0, y =…

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Q: Consider the equation y = 3*. a Complete the table of values. X y +- x+ -2 0 () Tab -1 a b 0 1 2

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Q: Find and classify any critical points of the function f(x, y) = -4xy + y² + 5x - 4y + 5.

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Q: Consider the Boundary Value problem 8²u 8²u + əx² dy² u(x,0) = x(7x), u(0, y) = 0, u(7,y) = 0, where…

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Q: Is f(x) = x / (1+sqrt(x)) uniformly continuous on [0,1] and [0, infinity).

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Q: The amount of foreign earnings (in trillions of dollars) kept overseas can be approximated by the…

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Q: QUESTION 4 a) Let (27¹) Calculate the products A. B and B. A, and the determinant det (A). b)…

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Q: Consumers' Surplus The demand function for a certain make of replacement cartridges for a water…

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Q: Convert to cylindrical coordinate. 1. z = x2 + y2

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Q: Use the definite integral to find the area between the x-axis and f(x) over the indicated interval.…

A: Given that f(x)=4ex-2[a, b]=[-4, 3]   The Formula for finding Area between the curve and x-axis.…

Q: Circulation and flux For the following vector fields, compute (a) the circulation on, and (b) the…

A: The given vector field F=-y, x and R is an annulus region r, θ; 1≤r≤3, 0≤θ≤π. We have to find the…

Q: For the matrix A, find an orthogonal matrix P such that P-¹APis diagonal. 1 1 0 1 10 [002] A = 01 01…

A: We orthogonally diagonalized the given matrix A.

Q: Consumers' Surplus The demand function for a certain brand of mattress is given by P = 400e-0.08x…

A: Given the demand function for a certain brand of mattress is given by…

Q: (1 point) Suppose R is the shaded region in the figure, and f(x, y) is a continuous function on R.…

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Q: A restaurant is upgrading its dining room for $20,000. The upgrade will bring in a continuous stream…

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Q: Moment of inertia about z is calculated as ³ ]]] (x² + y²) p(x, y, z)dV where p is the density…

A: Let E be the solid below z=18-x2-y2 and above the square [-3,3] x [-3,3]. And density is ρ=2. To…

Q: 21. Express the triple integrals of the function f=2x-y+z over the region bounded by the planes x =…

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Q: w is an imaginary root of unity. Prove that (i) (a+ba+ca²)³ + (a+ba² +ca)³ = (2a-b-c) (2b-a-c)…

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Q: (2) (b) (c) Use the Euclidean algorithm to determine the gcd of 85 Write down all the divisors of 85…

A: Let the given numbers are a = 85 and b = 135 (a)    From Euclidean algorithm.…

Q: 2 Find the length of the curve y = 3/2 from x = 0 to x = 4.

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Q: onsider the linear system A₁ = 0 v1 = ÿ₁(t) = a. Find the eigenvalues and eigenvectors for the…

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Q: A simple economy consists of two Industries: agriculture and manufacturing. The production of 1 unit…

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Q: Find the equation of the line joining the points (2, -8) and (5, 6)

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Q: QUESTION 5 Find the nullity of the matrix A = 1 1 1 6 1 234 1352 1 470

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Q: If (x + iy)³ = u + iv, then show that И V ---- + w y = (x² - y²).

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Q: K Solve the equation. In(2x+3) - Inx= In3

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Q: Let g(x, y) = -4.x³ + x² - 6.y² – 3.

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