Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C: boundary of the region lying between the graphs of y = x and y = x² – 8x

Q: Find the directional derivative of f(x, y) = sin(x + 2y) at the point (-2, -3) in the direction 0 =…

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Q: /hat is the area of the region bounded by the graphs of æ = y³ – 2y and DA = (3x – x² )dx DA = (? –…

A: Topic:- application of integration

Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: Find T(t) and N(t) at the given point. r(t) = 6 cos(t)i + 6 sin(t)j + tk; t= 2 6 0 , V37 1 T V37…

A: SEE EXPLANATION

Q: dx хV х2+2х-1

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Q: Write an integral that will give the area of the region in terms of dx (b) Write the integrals (do…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 00 In n n +…

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Q: II. Use the first fundamental theorem of calculus to find F'(x) .Write your final answer on the box.…

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Q: (y – Jx² + y² )dx -xdy = 0, when x = v3 and y = 1

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Q: A 25-year old woman burns 350 Gatorade is 55t calories during the tth hour. What is her net decrease…

A: A 25‐year old woman burns 350-60t cal/hr while walking on her treadmill. Her caloric intake from…

Q: Assuming that a DE has a general solution a+y= 3r +C, what is the particular solution at given the…

A: Explained below

Q: Consider the function f(x) = 4 – 7x² on the interval [- 5, 5]. Find the average or mean slope of the…

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Q: The sales function for a product is given by S(x) 124 + 37.8x? – 0.6x, wherex represents thousands…

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Q: Activity 1.5.2. A potato is placed in an oven, and the potato's temperature F (in de- grees…

A: This is a problem related to interpolation of the quantity. Based on the general formula we will…

Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

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Q: Find div F and curl F if F(x, y, z) = 10e*Y i – 6 cos yj+ 2 sin? z z k. div F= curl F=

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Q: Problem 37: Convert the following complex numbers from rectangular form to polar form: a. 4+ j3 b.…

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Q: Now, let's discuss the difference cases of solution to a given system of linear equations. There are…

A: Given problem :- Now, let's discuss the difference cases of solution to a given system of linear…

Q: What is the area bounded by the graphs of y = 8x and y = 16x 16? %3D O A = S*,- 1)dy O A = S*,(-1)dæ…

A: Topic:- application of integration

Q: Evaluate the iterated integral. /3 6. y cos(x) dy dx

A: I=∫0π3∫09y cos x dy dx =∫0π3cos(x) ∫09y dy dx  =∫0π3 cos(x) y2209 dx  =∫0π3 cos(x)812 dx

Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Find V x (V x F) if F(x, y, z) = 2xy j+ 6xyz k. %3D V × (V × F) =

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Q: Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108…

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Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 9y and…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

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Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Here we have to find the volume.

Q: II. MULTIPLE CHOICE: Choose the correct alternative that satisfies the given question. Write your…

A: We have to find correct option for the given questions.

Q: Given the vectors A = 3i – 5j + 2k and B = 7i + j – 2k. Find the vector projection of A onto B.

A: Given : A→=3i-5j+2kB→=7i+j-2k     To Find : Vctor Projection of A→  onto B→

Q: / Va2 – 1 ¢2 – 1 dx

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Q: Describe the graph of the equation. r = - 13 i+ (1 – 12 )j + t k O It is a parabola in the plane x =…

A: Given; parametric equation    r=-13i+(1-t^2)j+tk

Q: Determine the equation of the midline of the following graph. 2 -27 3 27 3' 47 3 3. '3 2 6. -1 -3 -4…

A: From the given graph we have to find the midline value

Q: Evaluate: Lī 3sin13 xda 512 1001 1024 1001 1024 1001 512 1001

A: Solved below.

Q: QUESTION 12 Eliminate the parameter to find a Cartesian equation of the curve. x-e'- 1, y - e Select…

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Q: The outside diameter of a thin spherical shell is 12 feet. If the shell is 0.3 inch thick, use…

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Q: ?

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Q: 2) Find of the following equation then simplify whenever possible. and dx dx2 x = 1+ Sin t y = Cos?…

A: The given parametric equation,   x=1+sin t, y=cos2t

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 3)i + tj, 0 sts1

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Q: Evaluate the following limit: lim x→2+ x – 2 O No answer text provided. |- 1/2

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Q: It is known that dx Compute . Simplify the final answer. 2х-у dx

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Q: Of all rectangles with a perimeter of lo meters, which one has the maximum area? (GIve both the…

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Q: The velocity function of a moving particle on a coordinate line is v(t) = t2 + 3t − 10 for 0 ≤ t ≤…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. %3D div F= curl F=

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Q: Find div F and curl F if F(x, y, z) = 7e*" i - 10 cos yj+ 8 sin² z k. div F=| curl F=

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y°x²j+2z²yk. %3D div F= curl F=

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Q: For each of the following, sketch the region enclosed by the given curves. Decide whether to…

A: In this question we have to find the area.

Q: Determine the vector field of F. F(x, y) = 8i – 4j

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Q: Find the deriva tive Of 6- sin (xy)+ e'

A: Note:- It is not mentioned in question for derivative find with respectvto what variable(x or y) so…