• Given f(x, y, z) = x² In(x + y- z), find f(2,4, 5). а. 0 b. 1 с. 2 d. 3 O a. b. С. O d.

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: If z = x² - xy + 3y2 and (x, y) changes from (3,-1) to (2.96,-0.95), compare the values of Az and…

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Q: Evaluate L[u(t-2)-(t-2)³} a. e-2s/s4 b. 6e-2s c. 6e-2s/s4 d. 6e²s/s

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Q: x,2,3) x ,x,1) P,(2,1,1) d ( P,(0,3,5) d (-

A: 1. P(x,2,3), Q(2,1,1), d(P,Q)=21 2. P(x,x,1), Q(0,3,5), d(P,Q)=5

Q: 2. (у? — 2ху + 6х)dx — (х? — 2ху+ 2)dy %3D 0, whenх%3D 1,у %3D2 = 3. v(2uv? — 3)du + (3и?v? — Зи +…

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Q: ir6 f(c)dz = 4 and , f(x)dr – 6, th then f(z)dz = Select one. O a -2 O b-10 Oc 2 Od. 10

A: We will let that the integration of the function f(x) is g(x) to solve the question.

Q: If y = хV3x , then y' is 3x A.V3x В. 1 + V3x + 1 D. х + V3x С. 2 2

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Q: 2. f(х, у) 3 а? —гу + у? then ,is

A: Given: fx,y=x2-xy+y2   We know that; The sum/difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1…

Q: The distance from the point S(1, 1,4) to the line x = 2- 3t, y = 1 + 6t, z = 4-t is Select one: A.…

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Q: Evaluate (3x²y + y)dx + (x³ +x) Select one:

A: Here we have to evaluate ∫(1,2)(4,5)3x2y+ydx+(x3+x)dy ............(1)  Here P(x,y)=3x2y+y and…

Q: Given u = 5) and v = (5, -4), calculate u· v.

A: u=<-4,5>, v=<5,-4>

Q: 2. For x 2 0, which equation is false? 3, 2 (x) = V3 А. X2 %3D B. (x³) = Vx3 c. (x) = Vx3 ( = С. X2…

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Q: Find Vz or Vw. 39. w = In /x² + y² + z²

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Q: Which of the following functions V(y₁, Y2) is a Lyapunov function for the dynamical system with…

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Q: 4. (a) If y = A + Bx + Cx2 and yo, yı, y2 are the values of y corresponding to x = a, a + h, a + 2h…

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Q: Evalu

A: Given, I=∫-12∫z2z∫0ydx dy dz To Find: Value of I

Q: dx 11. Evaluate , 1+x2 a. b. с. п d. 2n

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Q: (x* + 2y) dx – x dy = 0. ANS. 2y = x* + cx². %3D

A: We will find out the required solution.

Q: Y = -2X, then p(X, Y) = 1?

A: Solution

Q: If z = 3x² + y² and (x, y) changes from (1, 1) to (1.05, 0.9), compare the values of Az and dz. dz =…

A: The objective of the question is to compare the values of Δz and dz for the given function z = 3x² +…

Q: 26. 4 1+ n A. 1 В. С. e* D. -4 e Е. Divergent 4-

A: limn→∞(1+4n)n

Q: 7. (50 u) du + (3v - 7u) dv 0. ANS. (3v +u) = c(v u).

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Q: Find and a and дхду f(x,y) = x2 - y2 + 6xy + 4x – 8y + 2 a. b. f(x, y) = e*y + xy

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Q: Find the e v

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Q: 5. 9+ 16у? dy

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Q: Given the following question complete the integral and give the solution: Problem 1. Evaluate ,…

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Q: Q = 3x² + 5y² 1 , where x+y=8. Minimize

A: Qx,y=3x2+5y2 and x+y=8