9. GIVEN: QU || DA, QU DA. PROVE: AUXQ ADXA.

Q: Prove or disprove that if ∇ . F = 0 and ∇ * F = 0, then F = 0

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Q: The VVF Ct)= describes a helix. Find the tangent line to the helix at the point (0, 1, "/2).

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Q: Prove LHS=RHS

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Q: (a) If z = -1+i then determine | z| = r and Arg( z) = 0 and write z in polar form: z = r(cos 0 + i…

A: given z=-1+i comparing with z=a+bi a=-1, b=1 r=a2+b2=-12+12=1+1=2 therefore r=2 now argument z = θ…

Q: Let A = [–2 2]. If possible, find the entries of a matrix B that is NOT the identity, but still…

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Q: Show that fsint dt = using Laplace

A: To prove:- ∫0∞sinttdt=π2

Q: What is the laplace trasform of f(t)= (e^-4t)cosh4t

A: Laplace transformation is the integral transformation that converts a function of real variable to a…

Q: Assume that f and g are harmonic functions in R^n. Show that div(f ∇g − g∇f ) = 0.

A: Ans- We can start by computing the divergence of the vector field F = f∇g - g∇f:

Q: Consider the vector function r(t) that has unit tangent vector T(t)= 1 √1+5t² (1,1,2t), 0≤t≤2.…

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Q: Suppose you want to prove that ARST Theorem. If you know that ZR = LX, what else do you need to…

A: In ∆RST  &  ∆XYZ, ∠R≅∠X.

Q: Let y = cot (csc2x/x3+5). Find

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Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: The equation x''+ x = sin t has a bounded solution. true or false ?

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Q: Laplace £& cos'at} Cos al t 81

A: The Laplace transform of the function f(t) is represented as F(s), it is defined as ∫0∞e-stf(t)dt.…

Q: y" + 4y = cos(t−3)+4t, y(3)=0_y (3) = 7

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Q: Exercise 3 ry" + 2y' = 0

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Q: 14 5x - 21 16 2r + 3

A: When two triangles are similar then their side ratios are proportional.  So we get relation  MPQP=…

Q: Pind the ualue of e is an integrating facko of ly-y')+xy'so

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Q: Find the L^-1 iNVERSE LAPLACE f.) F(S) = 6s/s^2+25 + 3/s^2+25

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Q: Find the L^-1 iNVERSE LAPLACE h.)G(S) = s+7/s^2-3s+10

A: The given inverse Laplace function is, L-1s+7s2-3s+10. Laplace transform is used to solve the…

Q: O. Determine the area of the regien bounted by y-sy-andy- mark)

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Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt, n'=dxn, b' = d x b and…

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt. n'=dxn, h' = d x b and…

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Q: since ∆JKL~∆MKN, find LK

A: This question is based on similarity.

Q: Show that given that z = sin-12 дхду дудх

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Q: Proposition 11.5.1. If A and B are is defined, then matrices such that the matrix product (AB)=BT…

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Q: laplace{sin3t sin8t}

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Q: Assume that span(R) = RS. What is the payoff of the portfolio Zg = R¹ (RR¹) −¹ es when es € R$ is a…

A: Given: The portfolio, zs=RTRRT-1esTo find: The payoff of the portfolio zs.

Q: What is the relationship between the curvature tensor and the Riemann curvature tensor in…

A: The Riemann curvature tensor and the curvature tensor are essentially the same thing in the context…

Q: Find the L^-1 iNVERSE LAPLACE k.) G(S) = 25/s^3(s^2+4s+5)

A: Given: G(S) = 25/s^3(s^2+4s+5) We have to apply the inverse Laplace transform.

Q: F(s) = 60(s+5) (s+1)² (s²+68+25)

A: We have to solve using inverse Laplace transform.

Q: The line integral x dy – y dx Jc x2 + y? is independent of path.

A: Given integral is ∫Cxdy-ydxx2+y2.

Q: real

A: