Sketch the region R whose area is given by the iterated integral. *16 – y² dx dy 14 12 10- y 8. 4 2- 2- 8 10 12 14 11

Q: 1 de, where a, b, and d are real and a² + b² < d² a cos e + bsin 0+d

A: The given integral is: ∫02π1acosθ+bsinθ+ddθ Also given that: a2+b2&lt;d2.

Q: Evaluate the iterated integral.   6   2   x 2ye−x dy dx   1

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Q: S In?x dx = xln?x – 2xlnx + 2x + c %3D

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Q: 15.

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Q: Consider the parallelepiped with adjacent edges u = 8i + 7j + k v = i+j+ 2k w = i + 8j + 5k Find the...

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Q: Find the sum of 1, -1/2, 1/4, .... ∞. a. 3/4 b. 2/3 c. 1/7 d. 1/2

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Q: 4) Find dy given: y (1-x)(1+ x )(1+ x³ )(1+x*) dx d'y given: y= (5x -3X7x+x) 5) Find dx

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Q: 13. A cylindrical can is to be made to hold 1.5 L of oil. Find the dimensions that will minimize the...

A: This is a problem related to maxima and minima of the function. Based on the general formula we will...

Q: 180; 수i1 Question 8 Find the length and direction (when defined) of u × v. u = 4i + 2j + 8k, v = -i ...

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Q: If 8 (x) = | sinx dx and g |=3, then g (o) is equal to A -2 B D 4 2. 1.

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Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: f(x, y) = x2 + 20x + y² + 16y + 10 O f(-10, 8) = 102, saddle point O f(10, 8) = 502, local maximum O...

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Q: 2n + 1 Σ n tan-1 n n=1

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Q: (2y? + 2y + 4x²)dx +(2xy +x)dy = 0; when x =- 1 and y = 0 %3D

A: Let's find. 

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min....

A: As we know that; The expression for the volume of the sphere is: V=43πr3 Where; r is the radius of t...

Q: C. Bernoulli's Equation 5. (y* – 2xy)dx + 3x²dy O when y(1) = 0

A: We have given a Bernoulli differential equation.

Q: y = cot-1(4-3x2)

A: y=cot-1(4-3x2)differentiate w.r.t.xwe know that,ddx(cot-1x)=-1x2+1Therefore,dydx=-14-3x22+1ddx4-3x2d...

Q: Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ||...

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Q: 14. What is height of the isosceles triangle with the greatest area that can be inscribed in a circl...

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Q: Ssin*(x)cos²(x)dx

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Q: Given the curve ax? = y³, find the shortest possible distance between the curve and the point (0,8a)...

A: I am attaching image so that you understand each and every step.

Q: Let a = ci + jand b = 12i + 9j. Find c so that the angle between a and b is- 6' Round your answers t...

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Q: 1. y (x3 +3)5

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Q: Determine the equation of the plane that contains the lines Li and L2. L:x = 3 – t, y = 5+3t, z = -1...

A: I am attaching image so that you understand each and every step.

Q: Convert en extay?) JA O ver the region Q4. polar form and e to e Valuate let y= 7sino dA = rdrdo How...

A: ∫02π∫1e 2ln(r)(dr)(dθ) here we apply the ∫u*vdx rule ∫u*vdx = u∫vdx - ∫du/dx∫vdxdx so here 2lnr u = ...

Q: If y = csc² x +2, then ſ y dx = cot x + 2x + c %3D True O False

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Q: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then expres...

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Q: Consider the points A(3, –3, 3), B(4, –5,0), C(-3, –4, 0), and D(6, 2, –6). (a) Find the volume of t...

A: We have to find the volume and distance of given question 

Q: dx dy for 4xy-5x+4y = - 176, with the conditions dt = - 12, x=4, y = - 3. dt Assume x and y are func...

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Q: 2n +1 Σ n n tan-1 n n=1

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Q: 4. f(r, y) = + y + xy,find fay and fyz

A: Solve the following

Q: Question 3 Find all the local maxima, local minima, and saddle points of the function. f(x, y) = x3 ...

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Q: Find the critical points of f(x) = x³ – 21x² + 72x and use the Second Derivative Test (if possible) ...

A: f(x)=x3-21x2+72xFor critical pointDifferentiate the function f'(x)=3x2-(21×2x)+72f'(x)=3x2-42x+72Tak...

Q: 1. |x² In x dx; u = In x, dv = x² dx 2. 0 cos 0 de; u= 0, dv = cos 0 d0 %3D

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Q: Identify the vertices and foci of the hyperbola with equation x2 = 1 92 402 The vertices are The foc...

A: We will find the vertices and foci. 

Q: The line that passes through the points (4, –2,0) and (1, 1, 1) is parallel to which vector? Check a...

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Q: 9. (2y? + 2y + 4x²) dx + (2xy + x) dy = 0; when x = -1 and y = 0

A: As per our guidelines we can help you in solving only first problem. Rest of the problems you have t...

Q: For the demand function q= D(p) = 422- p, find the following. a) The elasticity b) The elasticity at...

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Q: up 4+y 10 -b -8 -7 -6 -5 -4 -3 -2 -1 3 4 5 6 7 8 10 -2 3 -4 -6- Give the equation for the ellipse gr...

A: We can find the equation of ellipse from the graph as below.

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. xy =...

A: Area , A = ∫∫R dydx or  ∫∫R dx dy.

Q: Find fx, fy, and fz. f(x, y, z) = In (xy) Z fx = z ln: fy=z In :f, = In (xy) fx :수:fz= In (xy) fx fy...

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Q: Sketch the region bounded by the given curves, then find its area. y = 2x - x^2, y = 2x^2 - 4x

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Q: S 3rsinh (x²) cosh(x²)dr

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Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

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Q: Consider the following planes. 5x + 2y - z = 44 X - 4y + 2z = 0 (a) Find the angle between the two p...

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Q: e*Vex-1dx ex+3

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Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers a...

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Q: Find a formula for the nth term of the sequence. - 2, 1, 6, 13, 22, ... Determine the sequence's for...

A: We have to find the sequence's formula in terms of n. 

Q: Evaluate (*. | (a? + 5) 0. OR Evaluate dr using Simpso o 1+x2

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Q: 1 )dx 4.

A: We will use substitution method to solve question 4.