2. Given f(x) = x² – x and g(x) = Vx – 6,x 2 6. %3D Show by evaluating the left hand side of equality that: 1 i) f(1 - x) = (x -: ÷) - ii) if f(x – 1) = 0 then x = 1 or x = 2 %3D

Q: (b) Solve for the optimum to the following problem using the Karush-Kuhn Tucker conditions: Optimise…

A: Solve the following using the Karush-Kuhn Tucker conditions: Optimise fx1,x2=x1x2s.t.…

Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: Find the most general antiderivative of f(x) = -3x – 7xL7. Note: Any arbitrary constants used must…

A: Topic = Integration

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A: We need to find solution of differential equation using homogenous.

Q: Maximi

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Q: 2. given that y = 0 at r=1

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Q: (1+,x£)u[ = (x)f I 'I %3D ,find f'(x). V(4x3 – 5x)2

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Q: If the joint p.m.f. of X and Y is given byh(x , y) = k(x+ y)2, x = -1, 0, 1 and y = 0, 2, 4.where k…

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Q: Let X and Y have the joint p. d. f. $2x for 0< x < 1; 0 < y < 1 otherwise f(x, y) = Then P (X + Y <…

A: Given  Information: Let X and Y are two random variables with joint pdf, fx=2x  , 0&lt;x&lt;1,…

Q: If u = f(x), then ſ dx x++2x²+1 k + C for some constant k . Compute kf(1). x2+1

A: We have to find kf(1) Given that: u=f(x),∫xx4+2x2+1dx=kx2+1+C  for some constant k

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Q: You know that: g(t) dt = 21 3 9(4) : %3D V3 g(9) = 3. V3 g'(x) Evaluate: da 9 + (g(x))²

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Q: Evaluate the bound of the error if the Trapezoidal rule applied to S (x)dx . Given that 5 k is…

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Q: 3. If f(x, y, z)= In xyz te(3.0²), find f,,f, and f-· 4

A:

Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

A:

Q: 1. Find the interval(s) wheref(x) = xe6* is concave down, if such an interval exists.

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Q: 2/3 Determine the length of x=| for 0<ys2. Assume that y is positive.

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Q: 4. Evaluate both sides of Green's theorem, for: F = (-x²y,xy²) where C is shown in the following…

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Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: The antiderivative of the function f(x) 4 + 11x is + 5.5z2 + c 4 5.5x + c -4 + 22.0x2 + c -4 +5.5x2…

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Q: 7. Let f(x, y) = 10x³y* + 21xy². Find fyyy. .3,4

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Q: 9. What is the antiderivative of f (x* – x³ + x² ) dx? - 1 r5 а. 5 1 1 --x4 +x³ +1 4 -3 с. X. 4 3 b.…

A: Given :   ∫ ( x4 - x³ + x²).dx    NOTE:   To find an Antidervative for a function f , we can often…

Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: Apply Euler method and Richardson extrapolation for h = 0.2, 0.1 the problem: and abtain g y' = ty…

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Q: The antiderivative of the function f(x)= 8+ 11z is %3D O -5 + 2.8r +c O -5 + 2.8x + c 11 +1.2x + c O…

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Q: 7. Given that f(z) = ar/² ++c*, find f'(x) .

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Q: The antiderivative of the function 4 .3 + 10x³ is, 4 f(x) - -4 .3 + 2.5x³ + c 4 -10 + 1.0xª + c -4 +…

A: According to question given f(x)=44.3+10x3We have to calculate the antiderivative

Q: 9. f(x.y. z) = In(x + 2y² + 322); P(-1, 2.4): u = -i- j - k

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Q: area bounded by f (x)=e^xand the x-axis between x=0,and x=2,use n=6 determine LHA,RHA,AND THE…

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Q: If f(x) = 1-x* , then an antiderivative F(x) could be Inx| -x А. 6-x C. 5x 3x 5 Inx| – x* 1+x° В. D.…

A: f(x) = 1-x5xAntiderivative F(x) = ∫ 1-x5xdx∫ 1-x5xdx= ∫1x-x4dx= ∫1xdx - ∫x4dx= ln x - x55 +…

Q: of fxyl = 3X-y+6 Subjected QI Find to x+y=4 extrume v alues

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Q: The antiderivative of the function 4 + 10x is. x2 f(æ) = 4 + 5.0x2 + c - -4 5.0x2 + c -10 + 2.0x2 +…

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Q: Suppose f(1) = 0,f(3) = 1,f'(1) = 2 , and f'(3) = -3. Evaluate Sxf"(x) dx. %3D

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Q: Let f(x,y)=2x²+y²-8x-6y+12. 1- Find Vf at (1,1). 2-Find the extreme values of f.

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Q: 2. Derive a formula to approximate S* s* f(x;y)dxdy yo xo Using Simpson's rule with x2 – xo = 2h ,…

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Q: . Suppose that we don't have a formula for g(x), but we know that g(2) = 4 and g'(x) = Vx² + 5 for…

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Q: What is the net crarop for fW={+5,05 as we qo from x=2 to X=5?

A: The given function  f(x) = x2 + 5

Q: 3. If f(x,y,z)= In 4 xyz Ite t3y:²s²) , find f,,f, and f..

A: Given that: f(x,y,z)=lnxyz4+e-(3xy2z2)

Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 fx) =4x

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Q: If f (x, y) = Vr3 + y3 In (x² + y³)esin(zy+y') + x°y+ 10 , then f. (1,0) O 4

A: Properties of derivative  ddxex=ex ddxxn=nxn-1 ddxsinx=cosx ddx(lnx)=1x

Q: Q4: Find the most general antiderivative F(x) of the function f (x) —D 2х7 — Зх5 — х?. - A F(x) = x³…

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Q: Find fCx) if flo)=0 and the tanGat (k,F CX) has ine af Slore x(x+2) a

A: Given for the function F(x), F(0)=0 and tangent line to F(x) at x,F(x) has slope xx2+23.

Q: What value of x minimizes C = 0.005x2 provided that C must be positive and x is within (0,1)

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Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 6., Given that= 1' + sy = ) and that y = 1 dr (a) show that for values of r close to 0, 1 when = 0,…

A: Let y(x) is a function. Then the expansion of Taylor series of the function y(x) at the point x=a…

Q: 3 The antiderivative of the function f(x) = + 9x is x2 -3 4.5x2 + c 3 + 18.0a? + c 6- + 1.5x + c 3 +…

A: