Evaluate the following integral using three different orders of integration. (xy + z?) dv, where E = (x, Y, z)| 0 s xS 6, 0 s ys 2,0 s zs5

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Q: 40. Let {r„}-1; {Yn}=1 be bounded sequences. Show that sup{r„}1+sup{yn}12 sup{rn + Yn}n=1 • 00

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Q: 7. Use the Divergence Theorem to evaluate ff(F n) dS, where S is the top half of the sphere r+y + z…

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Q: apply Gauss Elimination method to solve the equation? x + 4y – z = -5 x + y- 6z = -12 3x - y - z = 4

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Q: x²+2 dx x+1

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Q: 2. fct) = 3e +t C1-3t + 2t 2) -4t (1-3t + 2t2)

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Q: Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2.…

A: Substitute x3 for x in the given power series of ln1+x and simplify.…

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Q: . Show that there exists a real number 0 <x< 2 so that x' + 8x² – 10 = 0 -

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Q: -2 -2 0 3 4 4 -1 1 -1 | A = |0 -1 3 3 2 -3 4 -7 -2 0 9 -5-

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Q: 1 0 1 If B = -2 -2 -1 1 2 2 then det (B5) =

A: We have used determinant property.

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Q: Given: In(1+x) = >) (-1)". -xn+1 if |x| < 1. n+1 n=0 Compute the exact value of -1)"(n+2) 2n+1(n +…

A: Given: ln(1+x)=∑n=0∞(-1)nn+1xn+1 where x&lt;1To Compute: Exact value of ∑n=0∞(-1)n(n+2)2n+1(n+1)

Q: 4 k 2 -5 9 0 -4 -1 -9 -2 Let A = 0 0 k -4 6 0 0 0 2 6. 0 0 0 0 4 choose When is det(A) > 0? >

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Q: where p Let W be the set of all vectors of the form is a negative integer and q is a positive…

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Q: 4. Locate the centroid (x, y)of the following composite areas: -3 ft 3 ft I 1.5 ft 1 ft

A: Consider the given composite area and divide then into four areas as shown in diagram below,