8. Let x and y be vectors in 3-space, and suppose u is orthogonal to both x and y. Prove that u is also orthogonal to k₁x + k₂y, for every pair of scalars k₁ and k₂.

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Q: 6. If u = given by x = +2, where x+y+z= 1, prove that the stationary value of u is y b a+b+c' a…

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Q: f(x)=(1+ 3x)¹/4 ; (0.93)1/4

A: Follow the steps.

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Q: Find the 4th degree Taylor Series Polynomial for the function f(x) = ex centered at c=3.

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Q: b) Find the limit, if it exists, or show that the limit does not exist. 3x4 - 3y4 lim (x,y) (0,0)…

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Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

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Q: Given the points A(1,2,3,) and B(2,-2,1) Find the Vectors A and B with respect to origin. Unit…

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Q: Find the limit (if it exists) of the sequence (x_n) where x_n = sqrt(3n+2)-sqrt(n).

A: Here xn=sqrt(3n+2)-sqrt(n)               =3n+2-n               =3n+2-n3n+2+n3n+2+n…

Q: Ex3: Let X be a normed linear space. Use the Hahn-Banach theorem to prove the following statements.…

A: By the application of Hahn-Banach theorem,  we have to prove the following statements : i) For any…

Q: (e) zetiz 2² + a² Liv

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Q: Let V be finite dimensional vector space and let W c V be subspace with complimentary subspace W'.…

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Q: Consider the following. (-6.0). - 6 y = -4 -2 y 10 8. (0,7) 6 4 2 2 (a) Find the least squares…

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Q: Consider the system of differential equations x₁ = 2x1 + 0x2 y₂ = 4x1 +4x2 " where 1 and 2 are…

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Q: Consider the integral /1-x² 1- y² dy dx. i. Sketch the region of integration. ii. Give a geometric…

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Q: For the function f(x) whose graph is shown, what is the value of f(4)? -7 -51 7 X

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Q: C. USING SIMPSONS 1/3RULE WHEN N=10 AND N=15 1 0 x√1-x² dx

A: using simpson 1/3 rd rule for n=10 ∫abf(x)…

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: Box answer please.

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Q: 5. Let X be a random variable with a uniform distribution on the interval (0,1). Given Y = e, derive…

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Q: Question 1: Given the following languages: L₁ = {a,b,c,d} and L₂ = {1,2}. Evaluate the following…

A: Note: We are entitled to solve only one question at a time and up to 3 sub-parts only. As the…

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Q: Find the equation of the plane parallel to the line r = 2i + t(−4i + 3j + 8k) and containing the…

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Q: (a) Find the radius of convergence of the power series Σ(4" + 5") an

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Q: A solid of revolution is formed by rotating about the x-axis the area bounded between x = 0, x = 1…

A: 1] By Trapezoidal rule The value of the table x and y is  x 0 0.25 0.5 0.75 1 y 1 0.9896 0.9587…

Q: Question a) b) Let f(x, y) lim (x,y) →(2,-2) = I5-4xy² ²+2y Find the first partial derivatives of f.…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 6. We can evaluate π by use of the equation 0.5m-tan-¹(1/2)+tan-¹(1/3). Meaning of this equation is:…

A: Given that: 0.5π=tan-112+tan-113. 0.5π in radians is a sum of an angle corresponding to tan-112 in…

Q: 1. In each case, sketch a parent function or transformed function with the following end behaviours.…

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Q: Let f be a continuous real-valued function on the interval [a, b], and assume f(a) f(b). Let c be a…

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Q: Determine the inverse Laplace transform of F(s) =+ O le^(-9t)] + [5e^(-4t)] ● (e^(9t)] + [Se^(4t O…

A: We find required inverse Laplace Transform.

Q: Question a){ b) Let f(x, y) = - T5-4xy² x²+2y Find the first partial derivatives of f. Determine…

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Q: Use the parametrization r(x,z) = xi + f(x,z)j + zk and the following equation to derive a formula…

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Q: 3- Let X = {a, b} write a large Topology on X. 4- If A CX, find A' for (X.I).

A: (3) It is given that,  X = a, b. Then we have to write a large Topology on X. (4) It is given that,…

Q: 1-x² LITT 1- y² dy dx. (a) Sketch the region of integration. (b) Give a geometric interpretation of…

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Q: Consider the system of linear differential equations We want to determine the stability of the…

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

Q: Determine the bn of nth partial sum of the Fourier Series of the periodic function f(x) = -9x + 6,…

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Q: (i) Use the Divergence Theorem to calculate the surface integral ſſ F-dS; that is, calculate the…

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Q: Determine the mean and the rms values of the following by direct integration method a. f(t) = sint…

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Q: Directions: Translate each argument into symbolic form (using the suggested letters) and determine…

A: To find- Translate each argument into symbolic form (using the suggested letters) and determine…

Q: Solve the initial value problem y" + y' — 12y = 0, y(0) = a, y′(0) = −36. Find a so that the…

A: Given differential equation is y'' + y' - 12y = 0

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Q: Find the solution of the initial-value problem 11 y"" - 3y" + 16y' - 48y = sec 4t, y(0) = 2, y'(0) 2…

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Q: Find the absolute extrema of the function over the region R. (In each case, R contains the…

A: The given function is f(x,y)=x2-4xy+3, and the given region is R={(x,y)|1≤x≤4,0≤y≤2}. To Find:  (i)…

Q: Q3. a) Use the Gaussian elimination to solve following system 3x + 2y = 1 x=y=2

A: We have to solve the given system of equations.

Q: 2. (D² - 1)y = 2 1+ex

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Q: Consider a horizontal parabola of the form ay² + by + c = x where a = 0, and whose graph contains…

A: We have to find the equation of horizontal parabola  ay2+by+c=x The graph contains the points -1,3.…