9. Prove (1, sin z, cos z} is linearly independent in [0, 2x].

Q: Q1) Find the canonical form of these question : a) f(x.y,z) =F=x' y' z+x y° z" +x y z b) f(x.y.z)…

A: We are given: f(x,y,z)=F=x'y''z+xy''z''+xyz We are given the standard Form. F=x'y''z+xy''z''+xyz…

Q: the linearization of (fi,f2) = (x²y+ 3xy², 3x³ + 2xy) at (1,0) to approximate the value at…

A:

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: Z=x+y+ cos(x+y)

A: Given,        z=x+y+cos(x+y)

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A:

Q: Evaluate ∫ ▽f*dr Where f(x,y,z)=cos(πx)+sin(πy)-xyz and C is any path that starts at (1,1/2,2) and…

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Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

A:

Q: Evaluate I= √ (sinx+2y) dx + (6x+y)dy for the non closed path ABCD in the figure.

A:

Q: For which values of ß does {(1,0, ß),(1,2,–3)(B,1,0)} span R'?

A: If spans the same subset of R³, the vectors must be linearly dependent to each other.    Therefore,…

Q: 7. Which of the following sets of functions is linearly dependent on R0,2? (a) {6, z, sinz} (b) {1,…

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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Q: Differentiate w.r.to "x" y = xsin-1x +x/(1-x3)

A:

Q: linearise R = AT + BT

A: To linearise the below equation. R=AT+BT2

Q: Show that t, e^t, and sin(t) are linearly independent.

A: In the given question we have to show that t, e^t, and sin(t) are linearly independent.

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Either f,g,h € F(R, R) the functions f(x) = sin(x)^2 And g(x) = cos(x) and h(x) = sin(x). Show that…

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Q: 19. Determine whether each of these functions is a bijec- tion from R to R. a) fix) = 2x +I b)…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: II. Let f(x, y, z) = z° sin a + Determine 2 dydzərəz'

A: We know, ∂2f∂y∂x=∂∂y∂f∂x

Q: find Pn (Q'U R).

A:

Q: Determine whether the functions fi(x) = cos 3r, f2(x) = x, and f3(x) = cos² r independent on the…

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Q: Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at…

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Q: 8. Consider the complex function f(z) = x² + y² + 2ixy. a) Show that f'(31) does not exist. b) Show…

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Q: show that the L operator is linear for y" – 4y" + 2y' + y = x2

A: