EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

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Q: Question 17 The integral represents which quantity? the total mass with density F the length of the…

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Q: B. Find the slope of the curve at the given point. 16. 2x²-3x+1 at (2, 3) 17. =3x²-2x+1 at (-1,6)…

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Q: Evaluate the double integral: r2 Y To 0 √y¹/3 x7 +1 (Hint: Change the order of integration to dy…

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Q: Solve for the area bounded by the graphs of y = √√√x + 2, y = x + 2, x = 2, x = 4

A: Graph:

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Q: 12. Find the equation of the tangent line to the polar curve r = 2-sin(0) at 0 = 1/3. Draw.

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Q: n Express the function n, lim 21³ n→+∞ n5 i=1 and then find the limit. in closed form

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Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

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Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We can state the Divergence theorem .

Q: Evaluate (2a² y +9y³)dA, D is the region bounded by y 33522 a. 5 Ob. 4811 5 C. None of the choices.…

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Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

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Q: 1. dx (x - 2)3 EXOX

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Q: 3.lim X→π In(cos2x) (π - x)²

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Q: 5.) Simplify. Write "undefined" for expressions that are undefined. -2 -3 THE -6 -3 M

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Q: Use lagrange multipliers to determine the maximum and minimum values of f(x,y)= xy subject to the…

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Q: 1. Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v d) angle…

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Q: Determine if the function is continuous on the given interval. - 1. f(x) = √x² – 25 ; [−6, −5] 2.…

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Q: What is the component form of a vector with a magnitude of 17 and a direction of 125°?

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Q: 1 2 In|2|

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Q: The function √x² + 2x is equal to (x + 1)² + 1 Option 1 √(x + 1)² - 1 Option 2

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Q: A pilot heads his jet due east. The jet has a speed of 450 mi/h relative to the air. The wind is…

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Q: Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

A: To find the value of given double integrals.

Q: VII. - ) Let C be the curve consisting of the line segment from (0,0) to (2,0), the the portion of…

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Q: There are 30 emoticons. If 15 of the emoticons show hapinnes, 10 show confusion and 5 show anger,…

A: The answer is given below:

Q: 7. Find the general solution to the differential equation 2²y+2y=2¹/¹/2

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Q: Find the volume generated if the area between y = coshx and x from x = 0 to x = 1 is resolved about…

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Q: 4. [7.4 & 7.5] If... a = i +3j - 2k, and b=i-3j-k, and c=2i+j-k, then... a) Determine (ā- 2b) b)…

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Q: Suppose parametric equations for the line segment between (-2,-5) and (0, - 5) have the form: [ r(t)…

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Q: 8x²-x+8 x(x² + 4) 2 lnx + 6 in (x²+4)-4 Arctan ¹ (1) + C Option 1 4 Inx+6 In (x²+4)- Arctan (+C…

A: topic -indefinite integral

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Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A: To find the volume of the solid of revolution formed by rotating about the x-axis the region bounded…

Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y =…

A: follow next step

Q: Evaluate the double integral: To L 0 y x7 +1 y¹/3 x7 dx dy.

A: The given integral is: I=∫08∫y132yx7+1dxdy   So, The limit of the x varies from y13 to 2. The limit…

Q: Use the chain rule to find where st the pieces: z = x²y + xy², x=3-t³, y=3-t6

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Q: Find the volume of the solid generated by revolving the region bounded by y = 2x, y=0, x=0, and x =…

A: The given lines are y=2x, y=0, x=0 and x=4.   So, the bounded region is as shown below. Apply the…

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² + 5, the x-axis and…

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Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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