1. The set of functions (Po. P₁, Pn) in [a, b] is called a set of orthonormal functions, with respect to a weight function w(x), if (a) f(x) n(x) n(x)dx = 0 = xp(x)" (x) "dh (x)m of (a) (c) fw(x) 4₁ (x) 4₁(x) dx = 1 (d) None of the above

Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

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Q: Let f(z) = 4r- 12x +7 then f(r) is decreasing on Select one: O a (-00, -1), [12, o0) Ob [1,0) O…

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Q: Find the (natural) domain of the function x² - 4 f(x) = Vx² – 4 %3D O(-2, 2] O(-2, 2) (2, 0) O [2,…

A: Given that the function is          f(x) = (x2 - 4)/√(x2 - 4) Here we have to find the domain.

Q: The domain of the function g(t) = vt – 2 is O R-{2} O [2, 00) O R о (-о, — 2) n (? m)

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Q: The fixed point/s of the function g(x) = In(e²* – 3e* +3) + x on [0,1] is / are: Select one: а. О, 1…

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Q: A 1. What is (go f)(x) if f(x) = 2x + 3 and g(x) = ? %3D O (go )(z) = + %3D O (go f)(x) = + } %3D O…

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Q: Develop a first-order method for approximating f" (x) which uses the data f (x – 5h), f (x – 3h), f…

A: We have to develop a first-order method for approximating f''(x) which uses the data f(x-5h),…

Q: Let X = n(µ,4) and Var(2x) = E(4–7x) find µ.

A: Given: X ~ N (μ,4) So, V [X] = 4 V [2X] = E [4 - 7X]

Q: 4. Let f(x)= |x| and g(x) = x-3. (a) Determine the formulas for each of the related composite…

A: The composite function is defined as when the output of one function is used as the input of another…

Q: 1 The residues of a function f(z) are (:-4)(=+1)

A: Introduction :

Q: Use a computer algebra system to compute f(k)(x) for k = 1, 2, 3 for the following functions: (a)…

A: given,        a.  f(x) = cot(x2)b.  x3+1

Q: (19) Determine whether the following functions are injective, surjective, both, or neither. (a) f:…

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Q: solve the differenctil equation by undtermeind coefficients y'' +2y = -18x2e2x   y(x) = ?

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Q: 1. Determine f'(x) for each function below: f(x) = x2 – 2x + 3 f(x) = 7x3 · Vx %3D f(x) = x³ In x…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: Suppose f(x) and g(x) are real-valued functions satisfying g(2) = 4 g(3) = 5 g(4) = 2 f(2) = 4 %3D…

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Q: xercise II.2. let F(): R² R³ and G(): R² R² be given by (fi(x)) f2(x) f3(x)) F(x) = (iii) f3 and ere…

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Q: Let f(x) = In[x4(x +9)6(x2 + 4)3]. Find f'(x). f'(x) =

A: Given,

Q: The fixed point/s of the function g(x)= In(e-3e* +3)+x on [0,1] is/are: %3D Select orie: Oa. 1, 0 1…

A: given function is                                               g(x)=lne2x-3ex+3+x we have to find…

Q: 1.1 Let u(x; y) = 4(x2 - y2 ) - 5y. If f(x; y) = u(x; y) + iv(x; y) is an entire function, then v(x;…

A: Let u(x; y) = 4(x2 - y2 ) - 5y. If f(x; y) = u(x; y) + iv(x; y) is an entire function, then v(x; y)…

Q: in [1, 5] then the m for f(x) is

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Q: 20.) Find the linearization, L(x) ,of f(x)=x*+3x² values of f(x) when x=-1 , x=-1.1, x=-1.5 , and…

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Q: 1. Let N = {1, 2, 3,...} and let f: N→ N be a function given by f(x) = 2x + 3. (i) Find f(f(4) + 1).…

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Q: You have given a function A : RR with the following properties (z € R, n e N): A(n) = 0 , X(x+1) =…

A: Given that a function λ : ℝ→ℝ with the following properties x∈ℝ , n∈ℕ :   λn=0…

Q: 11. Let f(x) = x³ - 2x² + x-1 so f(1) = -1 and f(2)= 1. Let g be the X inverse of f; that is, g(x) =…

A:

Q: 4. Let f(x) = g(x) = x -5, k-(10) +7 = 10 and h (x) = find: ther b. Domain of h(x). c. (hof)(2). (Z…

A: (NOTE:   As nothing is mentioned, so all functions are taken as real valued functions.)

Q: (1) Suppose that f and g are multiplicative functions. Prove that the function F defined by I…

A: Consider functions f and g to be multiplicative functions. To prove that function F defined by…

Q: The Wronskian of the function y₁ = 1, y2 = x and Y₂ = x is

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Q: Let S={0,8,10,−9,−2}S={0,8,10,−9,−2}. Find f(S)f(S) in each of the following cases. a) If…

A: If f is a function from A to B and C be any subset of A. Then f(A)={f(y) : y is an element of A}