Evaluate tot? xe*< + y2 + 22 dv, where E is the portion of the unit ball x2 + y² + z2 s 1 that lies in the first octant.

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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question fo...

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Q: 2. Prove that g(x) = sinh x + x – 1 has a zero in [0, ln 2].

A: To prove that gx=sinh x+x-1 has a zero in 0, ln 2.

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A: The vector component of v along b is r=v·bb2 b The vector component of v orthogonal to b is u=b-r

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A: The tetrahedron with vertices P-3,2,0, Q2,1,-3, R1,0,1 and S3,-2,3

Q: Example 2: Find the parametric and symmetric equations of the line through the points (1, 2, 0) and ...

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Q: Consider the following equation. x² + xy +y° = 1 Find the value of y at the point where X = 1.

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Q: Find the area of the triangle with vertices P(1, 6, –6), Q(0,0,0) and R(3, 4, 1). NOTE: Enter the ex...

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Q: anx" + + a1x + ao An 4. If f(x) = bn with an #0 and b, #0, show that lim f(x)% = ... %3D .. + b1x + ...

A: As per the guidelines I am supposed to do the first question among multiple questions. So I am doing...

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A: We have to find area of Z=3.24 by Z table. 

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A: Given problem:- Find the derivative of f(x)=x2 e2.5x

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A: Given that 5-192+5-292+......+5-992Solution:

Q: a) Draw a neat and labeled diagram of the first six rows (n = 0,1,2,3,4,5) of the Pascal's triangle....

A: (a)  

Q: Example 3: Find the parametric and symmetric equations of the line passing through the point (-3, 5,...

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Q: 11. Evaluate dr if possible. If not possible, explain why.

A: We will evaluate the given integral in the following step  

Q: dy using implicit differentiation. dx 3. Find sec (xy?) = (cosh x)(tanh =+/9) + 2 csc¬1 (tan(y + 1

A: Given: sec3(xy2)=(coshx) (tanhx+sqrty)+2csc-1(tan(y+1)).

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A: Given: let f(x)=y1 and g(x)=y2 The graph is

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A: Topic:- geometry  In your answer x  intercept is not correct.  

Q: Determine whether the series is convergent ordivergent. the exact test that you Use. 00 Sinl 2. nこ1

A: To determine whether the given series is convergent or divergent.To write the exact test that you us...

Q: Find the area of the triangle with vertices P(1, 6, –6), Q(0,0, 0) an R(2,4, 1). NOTE: Enter the exa...

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Q: Consider the following limit A. Use a graphic calculator to find the limit B. Find the limit analy...

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Q: Given the following System of Differential Equations and its Eigenvalues and Eigenvectors 4 12 4 and...

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Q: Find the surface area generated b rotating the portion of the parabolic arc x = y^2 from x =0 and x ...

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Q: Find dy/dx of the following function using Chain Rule. y=(-3x5 +1)3

A: we use chain rule for differentiation y=(-3x5 +1)3 dy/dx =3(-3x5 +1)2(-15x4) dy/dx = -45x4(-3x5 +1)2...

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Q: Assume that the rate at which a cup of coffee cools to room temperature is proportional to the diffe...

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Q: Find the centroid of the region bounded by the curves: y = 2x – x² and y = x

A: Let, is the centroid of the region which is bounded above by the curve y=f(x) and below by the curve...

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Q: F(rn) = ¤n - | f(In) for For the function f(x) r2 + 2, write Newton's formula as In i 1 = f (In). so...

A: By the Newtown formula to find the Xn+1.

Q: Thus, for f(x): %3D x2 - 9 , if x 0 f-x) = %3D if x = 0

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Q: a) sin ) co () - c) tan 4) cot (- *) - ) me (- *) - sec

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Q: -3 sec-(VI) y = 4"(log, r)sech z

A: Given y=-3sec-1x4xlog2xsechx To find dydx

Q: A 3-meter long iron wire is cut in two. One piece is to form a square and the other a circle. b) Whe...

A: Let x  be the length of square.So the length of circle will be 3-x.Perimeter of square(P)=4s4s=xs=x4...