2. Show that e*, sin x, cos x are linearly independent using Wronskian Method.

Q: Use the chain rule and compute if z = x2 + xy³, x = uv? + w°y = u+ ve" O A. = (2x + y*)(2uv) +…

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Q: function fo) = 7X1+10x10x3_4 Qn Antiderivative of fo) is F(x) = Axn+ Bxm, CxP+Dx: A= 710 %3D where…

A: Solve the following

Q: Let D, be the linear transformation from C'[a, b] into C[a, b). Find the preimage of the function.…

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Q: Find the divergence of = ea + sin(xy) a + cos² (xz) a X O yey+x cos(xy) - 2x cos(xz) sin(xz) ọ xe…

A: U→=exyax+sin(xy)ay+cos2(xz)az

Q: 5. Find the linear appoximation for the funciton f(x, y) = (ro, Yo) = (3,0). x-y xy+1 at the point

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Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

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Q: 3) A hot cup of tea has temperature T(1) = 198 °F, one minute after it has been sitting on the…

A: To calculate the local linearization of the temperature at t = 1.

Q: Applying any method and show all the steps to determine whether f,(x) = cos 2x f,(x) =1 f,(x) = cosx…

A: We have to solve given question: Concept:

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

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Q: If xly then gcd(x,y) = y. إختر واحدا:

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Q: 1 1 T+ 2 1 B T+ - T(2)"-1 3(T, T)

A: To prove  βT+12,T+12=πT24T-11βT,T It is known that  βm,n=ΓmΓnΓm+n Now, for m=n=T+12,…

Q: What is the B of f(x, y) = tan (x3³+ 2xy)? [sec ² (x²y³+ 2xy] (3x²y² +2x) [sec² (x²y³ + 2xy ] (+²+*+…

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Q: hree solutions of the ODE x³y"" + 6x²y" + 4xy' - 4y = 0 are y₁ = x, y₂ = x-², and 3 = 3x-² + 8x.…

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Q: 1- Selve the follocwing first - order differential equation:- dy (xy+2ど)= xy + y a Xeて

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Q: fCx)=(1+x)* at X=0 is LUX)=1+ KX + "७) %3

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Q: f(x. y.z) = + xy + yz + Q8) Find the Linearization at (1,1.2)

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Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

Q: The set of all linearly independent solutions of D.E yY-y 0 is Select one: a. (1,t,e',e ) b.…

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Q: • The Doman of f(x) = 4 – Vx is 1. (2, 0) 2. [-2,0) 3. [2, 00) 4. [-2,2]

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Q: Solve the following Cauchy problem on half-line: Utt = Uxx u (0, t) = 0, u(x, 0) = x, ut(x, 0) =…

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Q: Given that f(x) = 2x + cos(x) is a bijective function, find (f-')'(1)

A: The function f-1 represents the inverse of function f. Therefore, if f-1x=y then x=fy represents the…

Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

Q: Q: Solve on white page clean and stepwise: Let f(x, y, z) = sinxyz, g(x, y, z) = x²yz, U = x²yi –…

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Q: Determine each of the following derivative values that involve functions that are defined in terms…

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Q: 3. If f(x, y) = xyz, X = and dø chain rule to compute Ər r sin(0) sin(p), y = :r cos(0) sin(), and z…

A: fx,y,z=xyzx=rsinθsinϕy=rsinθcosϕz=rcosϕ

Q: Show that the function f(x) = x’ + 1 is invertible from R to R.

A: First prove that the  function is one -one  let f(x)=fyx7+1=y7+1x7=y7x=y therefore, the function is…

Q: What is r' (x) when r(x) = In ? Select the correct answer below: O Pu) = - Sr+1 O rw = - Sr+1 x) = !…

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