Consider T(r1,12, Ia) = (371 – 212 + 4ra, I1 + 273, 12). Find T!. %3D

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Q: T(x,y, z) = x² + 2y² + z

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A: Given that F=y2, z2, x2 and the curve, C, such that, r=3cost, 3sint, 2t for, 0≤t≤4π. Differentiating…

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A: Given,                 f(t)=3e-2tcoshln2t

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A: f(x,y) = 3x²y² + 8x² + 4y² So, fx = 6xy² + 16x  &amp;, fy = 6x²y + 8y  &amp;, fxx = 6y² + 16 &amp;,…

Q: S = In sec 3x| + C 13. z sec² 3x dz %3D 3 - tag 3z,- å

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Q: df Compute if f(u) = u?, u(2) = -5, and u'(2) = -5. dx lx=2

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Q: Given F(r, s, t) = r(3s4 – 6t°), compute: Frst

A: This is a partial differential problem

Q: Q2: Prove that: d csc-(InVx) dx -

A: The main objective is to prove ddxcsc-1lnx=-12xlnxlnx2-1. It is known that ddxcsc-1x=-1xx2-1.

Q: Given F(r, s, t) =-r(8s³ +t³), compute: Frst

A: Given  Fr, s, t=-r 8s3+t3

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: 2. Find the correct value of c such that P (Z < c) = 0.4. %3D C =

A: According to the provided information, P(Z&lt;c) = 0.4

Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

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Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: AISO is isosceles with IS = IO. 22 = 2x+24, mZ3 = 6x– 52, %3D %3D nd mZ1. 1/ 3 bX 2 bx -52-180 S x-…

A: We have to solve the problem

Q: A- If y = e3x and y = e-3x , prove that: - d²y dx2 – 9y = 0

A: The solution for the above question is as shown below.

Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: Given F(r, s, t) =r(3s² + 9t°), compute: Frst

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Q: The mgf. of a r.v. X is (}+3) (+e) . Show that 9-x Ρ(μ- 2σ<X<με 20 - Σ (!) ( (3) P (μ- 2σ< <μ+…

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Q: Show that A Yk= V' Yk+r

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Q: Given F(r, s, t) = r(3s² + 3t²), compute: Frst

A: Solution of question is written in below steps.

Q: f(x, d,Z)cbxcly dz

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Q: Find f, and f, for f(x,y)=y In (2x+7y).

A: F(x,y) = y ln(2x + 7y) To find : fx and fy

Q: 4. If f(x, y)=: Vx² +y? 1 , find f, and f,.

A: Given data is : fx,y=1x2+y2  To find fx and fy

Q: Q4\ If A(x,y, z) = 3x²i + 3zj – 3xk find the Div (Grad A). %3D |

A: Explanation of the answer is as follows

Q: Gy Let Px) = x²/3, x. thens Rx) = x2/3 ×シ。 then: %3D O Find ê cx) ? 2 Gruphs off R and f

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Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: Find Duf at P. 2 f(x, y, z) = 6x³y°z°; P(2, – 2, 2); u = ;i + -k

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Q: Find EF in the trapezoid. x+6 A, 2x EF =

A: Given trapezium of ABCD, Given AD = x+6 EF = 2x BC = 0 From midpoint segment theorem, EF = (AD+BC)/2…

Q: Find the differential of the function. u = 5x7 + 7 np 35x6

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Q: : VERIFY USING CONVOLUTION 5(s? t1)

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Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: Q3: Find the value of n which F(x, y, z) = (x +y +z*)" to satisfy fxx +fyy+ fz= 0. 1

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Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: Find f f'Lx) = ZR? +aX-S and %3D to FlO)=4.

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Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

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Q: Consider f (x, y) = re63ry f-(x, y) = e63ry and fy(x, y) = %3D e63ry

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Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.

Q: [f(x)dx, if f(x) = Vx -k+1;k-13x <k,k = 1, 2,..

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