Evaluate S. F dr where F(x, y, z) = e'i+ (xe + e²) j+ye²k and C is the line segment from (0, 2, 0) to (4, 0, 3).

Q: A curve is given implicitly by the following equation .2 (x + y)² + x²y = 11 Find the slope of the…

A: Given the equation of the curve is  x+y2 + x2y = 11

Q: u+ 2v 4] = 1+ vw; w, and vw. w

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Q: 3. Prove: a) Bo(U,4,)=U,(BO4) b) BU(N,4)=N,(BU4)

A: a) B∩∪iAi=∪iB∩Aib) B∪∩iAi=∩iB∪Ai

Q: 2 2 y 6 L72 L48 yzdxdzdy =

A: Topic = Integration

Q: The issue of convergence or divergence of some series can be answered by several different…

A: NOTE:- AS PER BARTLEBY GUIDELINES, WE WILL ANSWER ONLY FIRST THREE PART OF THE QUESTIONS.

Q: 2. Suppose that the edge lengths r, y, and z of a closed rectangular box are changing at the…

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Q: If R is the region enclosed by 36 – 4x? - 4y² = 0 and 2x + 2y?- following sets gives R in the polar…

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Q: 1 In solving the antiderivative of f(x) = 2 - sin(x) by miscellaneous substitution, the substitution…

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Q: 31. Jul = 9.0 = 335°

A: Given query is to find the component of the the vector.

Q: Q38: If y = e2x sin 5x, then which of the following is true? (a) y" – 4y' + 30y = 0 (b) y" – 4y' +…

A: Given,            y=e2xsin5x

Q: So

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Q: 2) a> Determine the value(s) of k such tPhat g'u)= 5if g Cc) (x) x2-2 b) Write the equation of the…

A: In multiple question we are allowed to answer the first question

Q: (1) 8 6 2 "2 -2 -4 Increasing: Decreasing: Constant: 4.

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Q: tan5 e -y secseс е-У 9. S -dy ey

A: Since, the student has asked to solve question number 9, so we are going to solve only question…

Q: For the following integral, answer the questions below. ets dx (a) What should be your first step in…

A: Use first substitution then use integration by part

Q: x dx 24) (7x² + 3)5

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Q: y' = et ; y(0) = 2 find the general solution

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Q: Work Problem 1 (With integrity statement] Let R be the region bounded by yx+ 2, y=0, und x=2. Draw…

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Q: 00 n8" Use the ratio test to determine whether>. converges or diverges. (n + 1)! n=7 (a) Find the…

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Q: Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. 6s +…

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Q: Determine whether Rolle's Theorem can be applied to f on the dosed interval [a, b]. (Select all that…

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Q: Find the derivative of y. 30) y = In (sinh 5x) D . sinh 5x A) coth 5x B) 5 csch 5x C) 5 coth 5x

A: We can answer the question as below.

Q: •4 b (3x – 4)° dx = || f(u) du where (enter a function of x) = n dx (enter a function of x) — пр a =…

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Q: A rectangular garden is to be constructed using a rock wall as one side of the g and wire fencing…

A: We are asked to find dimensions of the rectangle.

Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

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

Q: Э) у%3 (3x2 + 5х +1)3/2

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Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim +00\ 5t2 + 6' 6t (?, ?)…

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Q: Determine if the relation defines y as a one-to-one function of x. OThe relation does not define y…

A: topic - relation and functions

Q: y" – 1/x = 0; y = x In x – 5x + 7 -

A: This question can be solved using the concept of first and second order derivatives.

Q: x2 Fusing trigonometric substitution, Jf(x)dx is transformed into n solving for the antiderivative…

A: Given problem:-

Q: For the integral, / tan'x sec*x dx, if we let u = tan x, what is the re-written form of the…

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Q: 0. f"(x) = 12x; f(1) = 2 and f'(1) = -2 3. ((a)

A: Given query is to find the function.

Q: For the function y In (6x) on the interval [1, 9], answer the following questions. (a) Give the…

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Q: Evaluate the triple integral xyz dV, R where R = {(x, y, z)| 0 < x < 3, -2 < y < 1, 1 < z < 3}.

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Q: Find the volume of the solid obtained by rotating the region underneath the graph of the function…

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Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

A: We can find the answers as below.

Q: Find:  ∫5-9x/ (x-1)(3x-2) dx  where x > 1.

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Q: S sin²x cos²x dx 1 sin 4x + C 32 O A none of the choices 1 1 ;sin 4x + C 32 8*+3, sin 4x + C O B

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Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: Work Problem 1 [With integrity statement] (! Let R be the region bounded by y=x+ 2, y 0, and x=2.…

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Q: dx J Evaluate: (x-4)(x-1) A None of the given choices 1 B x-1 +C X-4 (c) x-1 3ln X-4 + C 1 D X-4 + C…

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Q: Find the derivative of the function. 12) y = 2 secó x

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Q: Determine if the equation is separable. If so, solve the initial value problem. " e'y'(t) = t (In…

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Q: Let R be the region bounded by y =x+4, y=0, and x=4. Draw the region R, and evaluate the following…

A: Let's find.

Q: Surface Area All edges of a cube are expanding at a rate of 8 centimeters per second. How fast is…

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Q: line passes through the points P(6,10, - 1) and Q(8, - 10, -8). Find the standard parametric…

A: Given query is to find the equation of the line.

Q: In this question you must show detailed reasoning. Use the substitution u = 6x2 + x to solve the…

A: The given equation,      36x4+12x3+7x2+x-2=0

Q: Which of the points below correctly plots the point (-5, )? 12 3 4 56

A: We can answer the question as below.

Q: If y = x + ex, find dx/dt.

A: Given query is to find the derivative of the expression.

Q: x² + 64 Using trigonometric substitution, given dx, the simplified form of the integral is: […

A: