Use Stokes's Theorem to evaluate F. dr. In this case, C is oriented counterclockwise as viewed from above. Jc F(x, y, z) = z²i + 2xj + y²k v2 2

Q: (sinxy +xy cos xy) dx + x² cosx y d y = о

A: The solution is given as

Q: 2. Let T: R³ R³ be the linear transformation given by x1 + x2 + x3 +((:))-[ T X2 2x1 x2 + 7x3 -4x₁ +…

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Q: xy'=y+ IX2-y2 ху

A: We have to find the general solution of the given differential equation xy'=y+x2-y2 .

Q: 3.27.2. Let X be a metric space with metric d; let ACX be nonempty. (a) Show that d(x, A) = 0 iff x…

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Q: V. Find the slope of the normal line to the graph of g(x) = where x = 0. log₂ (1-x) sin ¹(x) + e² at…

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Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given the region enclosed by the curves x=cosecy, y=17π4, y=19π4, x=0 is revolved about the y-axis.

Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*10' part/m³), while the…

A:

Q: A ball is drawn at random from a box containing (6) red balls, (4) white balls and (s) bine balls…

A: Given Total number of Red balls = 6 White balls = 4 Blue balls = 5

Q: Elizabeth Swann and her husband consume wine (W) and books (B). Elizabeth's utility function is…

A: Elizabeth Swann and her husband consume wine (W) and books (B).

Q: ² - x ²² = y² dz ४x d²z Find the solution of xy' буду

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Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x = 3…

A: We want to find required polynomial.

Q: 18. Show that Σkind(k)³ = (Σk|n d(k))² for all positive integer n.

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Q: VIII. Suppose that f(x) is continuous everywhere and the graph of f'(x) is shown below. Do not…

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Q: III. Suppose that a function f(x) satisfies the following properties, together with the table of…

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Q: Equations with the Dependent Variable Missing For a second-order differential equation of the form…

A: Given differential equation is 8t2y''+(y')3=8ty'         (1) Let y'=v⇒y''=v' then (1) will be…

Q: For all positive values of a,b and c, determine the equilibrium points of the system * x1 = ax1 -…

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Q: Sketch the graph of f with emphasis on concavity. Label asymptotes with their equations and…

A: To sketch the graph of the function with the given detail.   −∞,−1 -1 −1,1 1 1,2 2 2,3 3 3,∞ f'…

Q: Let n P₁ P2 = ppp be the prime factorisation of an integer n > 1. 1: ti A 11. C.

A:

Q: is it divergent, convergent or absolutely convergent?

A: We have given a series ,  ∑k=0∞ sin2k+1π2 k3k+1! Here , sin2k + 1π2 = sinkπ + π2 sin2k + 1π2  =…

Q: limx→1 3 (x-1) tan(x³²-x) (x+1) sin²(2x − 2) -

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Q: f(x,y) = 3x-2y. R: the circle x² + y²

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Q: 1 Р ven as If th ● q 2 x are real and positiv llowing relations shc

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Q: 2. Specify on which intervals is f increasing/decreasing and where the graph of f is concave…

A: Given is information about the function f(x), f'(x) and f''(x) Then, to specify the intervals where…

Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*10' part/m³), while the…

A: Given that,The differential equation that governs the concentration (C) of the pollutantas a…

Q: Numerical Analysis (1) Let f(x)= ex2 + 4x³ . Find the third Taylor polynomial of f about xo = 2.…

A: Given function is fx=ex−2+4x3. We have to find the third Taylor polynomial of the given function f…

Q: Example 10.25. Solve the initial value problem dy/dx=x-y², y(0) = 1 to find y(0.4) by Adam's method.…

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Q: 1. Convert (-2.5 + j4. 2) into exponential form. 2. Convert 1.7e 1.2-j2.5 into rectangular form 3.…

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Q: Which one is a normal vector to the line which is perpendicular to the 8x - 3y = 9. A (8,-3) OB.…

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Q: For which value of k does the matrix have one real eigenvalue of multiplicity 2? k = A = 6 -8 2

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Q: V. Given: el3r-6-2, if x ≤2 13 f(x)=[2x - 5], if 2 3 √x²-9, 1. Determine if f is continuous or…

A: Given function is fx = e3x-6 -2   if  x≤22x-5  if  2<x≤3x2 -9  if  x>3 Domain for f(x) = -∞, ∞…

Q: 23 Find a 4 by 4 permutation matrix (call it A) that needs 3 row exchanges to reach the end of…

A: Consider the 4×4 matrix given below, A=0001100001000010 Here we need to apply 3 row exchanges to…

Q: If A = A. 3300 B.-900 OC. 900 3 find the (1,2)-entry of A300

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Q: 5. Consider that in 1915 that the population in the United States was 100 million. Suppose the…

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Q: A ball is drawn at randum. a bax Containing (6) red ball hallo

A: Given, a ball is drawn at random from a box containing 6 red balls, 4 white balls, and 5 blue balls.

Q: Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral 00…

A: Given function is f(t) = cos(t),0≤t<π0,t≥π

Q: VIII. Suppose that f(x) is continuous everywhere and the graph of f'(x) is shown below. Do not…

A: 1) since for maximum or minimum values of x of the function f(x) ,f '(x) =0, so for x=4 f has…

Q: Find the unit tangent vector of the given curve. r(t) = (7t cost-7 sin t)j + (7t sint + 7 cos t) k…

A: The given question is related with unit tangent vector. Given that,               rt = 7t cost - 7…

Q: II. Find Do not simplify your answers. dy dx tan-¹(cosh.r) 2. y= (sin²x) (sech x)sec z [use…

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Q: 3. Suppose that we have the following four tuples in a relation S with three attributes ABC:…

A: Given: Let us consider the four tuples, ABC:1,2,3,4,2,3,5,3,3,5,3,4. Let's determine the…

Q: a x In the experiment of tussing a fair coin is the randam variable giving 3 times the number of…

A: Given three fair coins are tossed. So PX = 0 = 18P(X = 1) = 38P(X = 2) = 38P(X = 3) = 18

Q: 10. Prove that 7/2 75/2. sin 0 cos (cos a cosec 8) de 10 T 2 (1-cos a).

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Q: H-w.4 Find the volumes for the following solids whose heights are defined by Z(x,y) and bases are…

A: Volume bounded by xy-plane

Q: 6x-25x+8x+43x--8x-12 (3x4-11x3 +9x²-11x+6) (9x² +12x+16) + C(3x+2)+D 9x²+12x+16] Find f - [Ax+B x²…

A: Given integral is      (1) Its reduction is ∫Ax+Bx2+1+C(3x+2)+D9x2+12x+16dx We can write it as…

Q: Example 10.27. Find an approximate series solution of the simultaneous equations dx/dt = xy + 2t,…

A: Here, we need to find approximate series solution.

Q: For the equation, 9x² +8√3xy+y²-8=0, complete the following questions. a. Rewrite the equation in a…

A: The general form of a conic equation is Ax2+Bxy+Cy2+Dx+Ey+F=0.  The value of B2-4AC>0 decides the…

Q: Let S₁ be the surface generated by z -4 = -y revolved about the z-axis. Let S₂: x² + y² = 4. Draw…

A: Given: Let us consider the S1 surface created by z-4=-y about the z-axis. The S2 surface by x2+y2=4.…

Q: Lazio Airline has the following flying routes: Rome (1) to London (2) London to Rome Rome to…

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Q: 4: 4d³y - 13+6y=0 dx3

A: Given differential equation: 4d3ydx3-13dydx+6y=0To find: General solution of the differential…

Q: Test the series for convergence or divergence using the Alternating Series Test. 1 1 1 1 1 In(5)…

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Q: A faire dice is tossed twice -11 LI Pace

A: Given, a fair dice is tossed twice.