Show that function f:R R, f(x) = 2x2 – 4x + 3 admits primitives on R and determine a primitive of it Calculate the primitives of the functionf: D R, using the table of undefined integrals and their properties a) f(x) = x-5 b) f(x) = sinx - 3e* + 5 c) f(x) = 2x? + 8 - ! d) f(x) =Vx %3D e) f(x) = 6x4 %3D ) f(x) = (x- 4)²+2 For the function f: R- R, f(x) = find the primitive of F whose graph passes through the point M (4; -1) Calculate undefined integrals, applying known integration methods dx V1- 7x (2х — 1)lпxdx Show that the function F: [0; +o) → R, F(x) =x, it is a primitive of function f: [0; +0) - R, f(x) = Vx. %3D

Q: Define F : R → R and G : R → Z by the following formulas: F(x) = (x^2)/3 and G(x) = ⌊x⌋ for every x…

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Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: Letf :Z→Zbedefinedbyf(x)=x^2 +1,and letC ={1,2,3}. Find f (C), f ^−1(C), f ^−1(f (C)) and f (f…

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Q: 77. Show that if f is a quadratic polynomial, then the SDQ at x = a (for any h + 0) is equal to…

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Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: Finel the ralves of a anel b such that the function aV5-x tb-1 it Hax cos(TT Ix) 9 +1+ b(x²-7)…

A: Note: There is an error in question, for the given function a has 2 values but it cannot be possible…

Q: The psd of X(t) is given by [1+ @? for | @|<1 Sxx (@) otherwise Find the autocorrelation function.

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Q: What are the necessary and sufficient conditions for a complex-valued function to be analytic in a…

A: Analyticity is a fundamental concept in complex analysis. A function of a complex variable is said…

Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: • Let a) f: IR₁ ->R₂ & f(x) = - = b.) f: IR₁ → IR₂ & f(x) = 2x² +7 EXC 3X 3 2 Do some appropriate…

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Q: Show that f(x) = 1/(1+x) is analytic on (-1, ∞).

A: To show that f(x) = 1/(1+x) is analytic on (-1, ∞), we need to show that f(x) has derivatives of all…

Q: 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²² +₁ Z-1 2) f(z) = 3z²…

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Q: Find all poles, their order and their residues for the function f(z)=(z+1/z-1)3  ( z+1 in numerator…

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Q: consider the function f(2)= x³ +32+1 in the interval [-3,3]; we can say a) f has no zeroes in the…

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Q: Prove that f(x)=x^3+x-1 has a root in the interval [0,2]

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Q: Write a polynomial function of least degree with integral coefficients that has the given zeros. 23)…

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Q: By the Fundamental Theorem of Calculus 2+x² Newton-Leibnitz, Theorem) evaluate √x dx

A: We have to evaluate  the given integral  ∫142+x2xdx  by using fundamental theorem of calculus.

Q: Let f(x) = e^x Find the polynomial H3(x) of degree at most 3 such that H3(1) = f(1), H3(2) = f(2),…

A: Given: Consider the given f(x) = ex .Using a (generalized) divided-difference table, find the…

Q: z is a complex variable z=x+iyFind all points of discontinuityf(z)=(3z^2 +4)/(z^4 -16)

A: To locate the points of discontinuity of the given function f(z) of the complex variable z.

Q: What is the residue of the function f(z) = (z^2 + 1) / (z^3 - 2z) at the point z = i?

A: We have to calculate the residue at

Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: Orthogonalize {1, t, t²} in P₂ (R) with 1 (f, 9) = ["ª, f(x)g(x) dx. -1 Then normalize each one so…

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Q: Find the derivate of the function: a) • f(x) = 5x + 4 f'(c) = 2 d) • f(x) = (5x²³²-4) (8X+S) b)•…

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Q: Express (-2/3 + j2) in rectangular form.

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