Solve the differential equation Integrating Factor by Linear Equation: dx + xcoty = ecosy dy

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Using appropriate substitution 9x2 – 4 dx X is equal to

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Q: Solve the differential equation Integrating Factor by Inspection: (2y – 3x)dx + xdy = 0

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Q: fu)=Sin(x) aニT R=?

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Q: Quéstión lốf 4 f(x) = (x³ + 2x)(2x – 1)5

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: The following telescoping series 00 1 Σ- en+1 – en+2 n=1 converges to Ve the above none of them…

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Q: Find curl (7z i + 8x j + 9y k). curl(7z i + 8x j + 9y k) = ( i )i + ( i )j + ( i )k

A: This question is related to vectors, we will solve it using given information.

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 6tj – 6ik) dt

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Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: Given: x=4y, x=-4y, y=1   From the given curves the bounded region is as shown below;

Q: y = 3x - x2 and y = 2x 11 %3D

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: This is a problem related to vector calculus. Based on the general formula of green's theorem we…

Q: y" + 2y' + 5y = 3 sin(2t)

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Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

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Q: For the given vectors a and b, find the cross product a x b. (2, 0, -3), b = (2, 1, 0) a x b = %3D

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Q: Obtain the limits of the following functions: (2sinx-sin2x 1. lim x-sinx

A: To evaluate the limit of the function.

Q: Find the partial derivatives of f(x, y) = 5x°y². %3D (g) fz(1,2) (h) fy(1,2) =

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Q: Describe the graph of the equation. r = 10 sin 6t í – 10 cos 6t j

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Q: 5. y = (x+7)(5x- 2)

A: Given : y=(x+7)(5x-2)   To Find : Derivative of the given function.

Q: For the given vectors a and b, find the cross product a x b. =(3,0, -1), b = (3, 2, 0) a %3D a x b =

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Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

Q: Find div F and curl F if F(r, y, z) = 2e*"i– 9cos yj+ 4 sin² z k. div F= curl F=

A: Given: F(x,y,z)=2exyi-9cosyj+4sin2zk

Q: Find the area bounded by the curve r= 2+cos θ

A: Given problem:- Find the area bounded by the curve r= 2+cos θ

Q: 7. lim vx2 + x + 1 – Vx2 + 1

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Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: Find the indefinite integral. 17 dx +C

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Q: Find curl (6z i + 7x j+ 9y k). curl(6z i + 7x j + 9y k) = ( i )i + ( i )j + ( )k

A: Explanation of the answer is as follows

Q: 1— 2 — е-7 lim 2.x e sin(8x) →-

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Q: Solve for the derivative of the following composite functions. f(g(x)) = (x + 4)5 1.

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Q: 3.) ž sin'(x)dx

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Q: On what intervals is the function f(x) = continuous? x(x - 1)(x- 2) 1. (-00,0) 2. (0,1) 3. (1,2) 4.…

A: First draw the graph Uasing limits and the check the countinity of this function

Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

A: We have to find the values of vector valued functions.

Q: Find three positive numbers whose sum is 48 and such that their product is as large as possible.…

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Q: (2a+1)(x–2) lim x00 (3x-1)(x+2

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

Q: k(x) = 22.8 cos (0.3(x – 72.29)) – 2.9 1(x) = 0.5e (-x+82.762) - 25.7

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Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

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Q: Find V· (V × F) if F(x, y, z) = 7 sin xi + 5 cos(7:x – 8y)j + 6zk. V . (V × F) :

A: F(x,y,z)=7sinx i+ 5 cos( 7x-8y)j+6zk

Q: A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy…

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Q: ||r(t) × r"(t)|| Use the formula k(t) = to find k(t). 13 r(t) = eti+ etj K(t) :

A: Given r(t)=e5t i + e-t j

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1.

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Q: 2. Vector v has a magnitude of v53 and a directional angle of 164.055°. Select the response below th…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = – 2tj %3D

A: 1st derivative, 2nd derivative, dot product and cross product are evaluated.

Q: 7. S x4 sec (x5 - 9) dx 8. S tan 3 x dx

A: Question 7 and question 8 are solved.

Q: Describe the graph of the equation. r= (5 - 31) i - 10:j O tis a line in 2-space that goes through…

A: This is a problem related to vector. Based on the general formula and concepts we will answer the…

Q: Let F(t) = < 5t + 5, t - 2t, 2 In < 5t' + 5,f – t, a. Determine the coordinates of the point on the…

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Q: The equation y? = cx is a general equation of A. y' = 2 B. y = 2x 2x C. y' = y y D. y': 2y O A NONE…

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Q: The smaller the curvature in the bend of a road, the faster a car can travel. Assume that the…

A: We need to find speed at given point.

Q: Definite Integral. 2.) S x²(2x³ + 1)*dx 4.) x?e*dx 6.) f- xp:

A: To integrate.

Q: Find div F and curl F if F(x, y, z) = x°i – 10j + yzk. div F= curl F=

A: To find the divergence and curl of the following vectorF→=x9i-10j+yzk

Q: 8 – a? if – 2 2 between O 8 and 16 O O and 8 O 16 and 24 O 16 and 33

A: Given problem:-