Find div F and curl F if F(x, y, z) = xz°i +2y°xj+62

Q: Find the limit of the following sequence or determine that the sequence diverges. 15 Select the…

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Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: A curve in the plane is defined parametrically by the equations x = t +t and y t* + 2t2. An equation…

A: The equation of the tangent line is: y-y1=mx-x1 Where m is the slope of the tangent line. And The…

Q: S (1/(X(Im)*) dx X(Inx)

A: LetI=∫1xlnx2dxLet u=ln(x)differentiate 1xdx=duI=∫1xlnx2dx.I=∫1u2du.I=∫u-2duUse power…

Q: 2.2 State the identity that validate sin x = 3 cos x- and hence show that 6+9/3 tan x = [10] 23

A: Follow the procedure given below.

Q: +4x –1 dx x' - x 2.

A: As per our guidelines we can help you in solving only first problem rest of the problems you have to…

Q: 10 10 If f (x) dx=17 and f (x) dx=12, then f (x) dx=5 . 8. (A) True (B) False

A: To determine whether the given statement is true or false.

Q: Find the volume between the cone y = Vx² + z² and the sphere x2 + y² + z² = 25. volume =

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Q: x + 2y = 1 , x – 2y = 8 . Credit will be given for use of the method, and not for the so y =-7/4.

A: We will solve using cramers rule.

Q: Find the absolute maximum and minimum values of the function on the given curve. Function: f(x. y) =…

A: Let's find.

Q: 1. S 2x-6 すdx (x-7)5

A: Solution:

Q: 6. Given f(x,y) = x² – 2xy² – 4xy + 5. Find all the critical points of f and determine the nature of…

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Q: Find curl (8z i + 9x j+ 10y k). curl (8z i + 9x j+ 10y k) (i )i + ( i j + ( )k

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Q: Find r'(t). r(t) = (tan¬(11t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

A: Here, the given vector function is: r(t)=(tan-1(11t))i+tcos(t)j-tk

Q: tan 0 d 30. dO sec² y dy

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Q: dy Given a first order differential equation dx Зx* у + tan y x' +xsec' y Q3

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Q: Given a differential equation dx with the initial condition, y cos (2x) 8

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Q: Determine the vector field of F. F(1, y) = 9i – 3j

A: kindly attached following graph.

Q: dy for x'e*y Find dx sin' ( 3x) + In (y) by using implicit differentiation.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt' the product directly and…

A: r1(t)=cos⁡(t)i+sin⁡(t)j+6tk,r2(t)=5i+tk Given:  ddtr1(t)⋅r2(t)=r1(t)⋅dr2dt+dr1dt⋅r2(t) and…

Q: Let v=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

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Q: Obtain the inverse transform of the following 2s-3 1. s2-9 10 (3s2+12) + (s²–25) 3s-2 3.…

A: As you have asked multiple questions so I have answered only first question as per the…

Q: X+3 Q4) Find the integration by using: dx 2x3-8X

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Q: e2 º In(2) dzr

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Q: completely

A: We will solve the integration.

Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x? N(x, y) = x² - 2y (I): (2xy – 3x )dx…

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Q: Calculate the limit of the following recursive sequence ao = 1 an+1 = V1+ an Hint: Prove that an is…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: ||r(t) x r"(t)|| ||r'(t)||* Use the formula k(t) to find k(t). 13 r(t) = 10 cos(7t)i+ 10 sin(7t)j+…

A: Given; r(t)=10cos(7t)i+10sin(10t)j+3tk

Q: 15 15-2 0

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Q: х- у 3. f(x, y, z) = y? + а. f(3, —1, 2) b. d. f(2, 2, 100) с.

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Q: (-5 S + (0.9)" | lim

A: Given query is to find the value of the indicated expression.

Q: differential cgnatuin as A. Identify the given to the dependent variable, degce z the eguati degre 3…

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Q: 12 For the given function y 3 cos ( 0 2 state the following (show al Work) a) Amplitude b) Period c)…

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Q: Use the formula k(t): |r'(t) × r"(t)|| to find k(t). r(t) = ti + t°j K(t) =

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Q: 2. fx Arctan xdx

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Q: y = x(x2 – 4)

A: We have to find the area of the shaded region.

Q: Solve 6+ 3+ ニ 2-t-26 3-7++10 +

A: Please refer to the image below

Q: 1. Sam throws a stone into a river. This caused ripples in the form of concentric circles. The…

A: Given problem:- Sam throws a stone into a river. This caused ripples in the form of concentric…

Q: Q5) Find the integration by using (by part method): S e3X sin X dX

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Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: 2t +1 lt +8 -dt + 4t +4t 3

A: Let's find.

Q: Find the curvature and the radius of curvature at the point t = 0. I = e' cos(t), y = e' sin(t), z =…

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Q: 11 a) Use the rational root theorem to find the possible rational roots of 12.r -8r-3T+2=0 b) List…

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Q: Find r'(t). r(t) = (tan(10t))i+t cos(t)j – VEk NOTE: Enter your answer in terms of i, j, and k.…

A: Given problem :- r(t) =(tan-1(10t)) i+t cos(t) j-√tk Find:- r'(t)

Q: `x² In x dx

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Q: For the curve y = f(x) = x², 0 < x < 2, its length is 2 dy` dx - {(aV17+ In (4 + v17). VI7). L 1+…

A: Apologies for the inconvenience. The correct solution is given below: Given that y=x2 Hence, dydx=2x

Q: ; Test the following series whether it is convergent or divergent (show all your works) n2 +7 a) 2…

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Q: Evaluate the following integrals. 2 (a) S(csce)(1 + sin´e + sine cot + sin¯0 + sin0 cot¯0 ´e)de

A: Solution is given below:

Q: (7 cos° t dt 2

A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

Q: 4. Consider the matrix А 5 2 One of the eigenvectors of A is given by [1 -1]'. Find the eigenvalues…

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