Show that the vector field A (3x?z + y?)a,+ 2xya, + x³a, is conservative. %3D

Q: I Find the second derivative (y") of the following functions and simplify the final results. 2sin x-...

A: topic - double derivative of a function

Q: Question dty of y = -10 sin (x) – 8 cos (x). Find %3D dx4 Provide your answer below. d FEEDBACK MORE...

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

Q: The slope of the tangent line at any point (x, y) on a curve is 2/x. If the point (9, 3) is on the c...

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Q: (2– sec²x) ln (# /e)scc³x sec(3A – x) What should be the value of A for to be integrable using the f...

A: Let's find. 

Q: Find the area of the region bounded by the curve ,2-4r and the lines x = 1 and x = 4. 21/2 square un...

A: The given question has been solved in detail and option B is the correct answer.

Q: 10 -dx may be writen as Ala secB" + tanB"| + C where A, B, and C are constants not equal to zero. Ev...

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Q: 3 dx Evaluate the J 2+81 improper integral:

A: We need to integrate∫-∞∞3x2+81dxWe know that ∫1x2+a2dx=1atan-1xa+C ---{1}

Q: dx - = In[F(x)]+C. What is F(/3) if C= 0? For (x+x³) (x Tan-'x+ 1) A B 3 c) 6 D) 3 + + -15

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Q: the brakes on a car give the car a constant negative acceleration of 2k m/s2, where k is a positive ...

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Q: (cos(2x) – sin(2x) cos(2x)) cos(x) – sin(x) For -dx%3D +C. What is F (x)?

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Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?, where k is a positi...

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Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: ·sec-x)" sec'x 23. What should be the value of A for -dx to be integrable using the formula | u" du?...

A: the integration of the integral is (2-sec2x) eln(pi/e)sec3x/Sec(3A-x).

Q: cos2x - sin2x cos2x -dx =-F(x)+C• For What is F(x)? cosx – sinx 2 sinx + -cosx+ cosx + -sinx 3 3 2 s...

A: Using cos(2x) =cos2 (x) - sin2 (x) 

Q: Which of the following is an improper integral?

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Q: 7. Find all solutions to the equation sin r = –0.7 with -1 <I < 10. 8. Find the equation of one of t...

A: Topic:- derivatives and equation of line 

Q: If Fx) is an antiderivative of x2 +x1, then what is the value of F(1) - F(-1)? 3

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Q: Question 13 Find the area of the region bounded by the curve y=1- and the x-axis. 6. A 4 square unit...

A: A detailed solution is given below

Q: Find an equation of the line which is tangent to the circle z + y - 4x + 6y – 12 = 0 at the point (5...

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Q: Which of the following is an improper integral? In(x4+1) dx dx x2-x- 2 dx 2x+ 8 2 In3e COSX dx xe -2

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Q: Find the area of the region bounded by the curve y=1. and the x-axis.

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Q: Find the equation of the curve for which dx2 = 6- 9x and which passes through the points (0,–1) and ...

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Q: Let f(x)=4x^2lnx f'(e^3)=

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Q: (a) Let (x, yo) be a point of the plane, and let L be the graph of the function f(x) = mx + 6. Find ...

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Q: The antiderivative of f(x), denoted by F(x), exhibits an odd symmetry i.e., it satisfies the propert...

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Q: - 1) ? du

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Q: x2-4x+1 2. Evaluate lim X-1 x-1

A: The given question has been solved in detail.

Q: Find the derivative of the function. 3. 2x2 - 5 =イ 4- x %3| y' = ||

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Q: dx -In[F(x)]+ C. What is F( 3) if c = 0? For (x+x³)(x Tan-!x + 1)

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Q: (2-sec?x) lnae sec(3A -x) sec'x dr to be integrable using the formula What should be the value of A ...

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Q: dx For -= In(F (x))+C. What is F (/3) if C=0? (x+x³) (xtan-1(x) + 1)

A: Let's find. 

Q: sin-cos-sine de has the form --F(0). 2 The resulting integral of +C. What should be the value of e t...

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Q: 8. W ( 10л 3 9. W W (–317) 22л 10. W 3

A: Since there are multiple questions the first question is answered as per our guidelines. kindly repo...

Q: A. Use the tabular method to evaluate the following limits. Set three values of x from each side. Ro...

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Q: In (rle) sec³x (2– sec²x)«ma/2)sec³x What should be the value of A for dx to be integrable using the...

A: we have to find the value of A. 

Q: m,n, p,q,r and C are constants not equal to zero. cos x - esin(x) + e$in(x)+x esin(x) dx Evaluate m ...

A: We will find the value. 

Q: If the brakes on a car can give the car a constant negative acceleration of 2k m/2 , where k is a po...

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Q: cos2x – sin2x cos2x For - dx =-F(x) + C. What is F(x)? cosx – sinx 3 A (cscx- secx)3 2 B sinx + =cos...

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Q: Question 12 If F(x) is an antiderivative of x2 +x1, then what is the value of F(1) - F(-1)? O-1 3

A: If Fx is an antiderivative of x-2+x-1, then to determine the value of F1-F-1.    

Q: dx - = In[F(x)]+C•What is f(/3) For if C = 0? (x+x³) (x Tan-!x+ 1)

A: A detailed solution is given below

Q: sin-cos-sino do? 2 2 What is the integrable form of

A: Given that,

Q: 2744 A computer is purchased for $2744. Its value in dollars after t years can be approximated by V(...

A: We will solve the first part of the problem bu putting t=3. And for second part we will derivate the...

Q: What is the equation of the circle that passes through points (2, 3), (6, 1), (4, –3)? x? – y? – 6x ...

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Q: 4 dx Evaluate Зх— 12

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Q: dx = In[F(x)]+C.What is F(3) if C= 0? For %3D (x+x³) (x Tan-x+ 1) A B -1 + 3 D -15 -15

A: Please see the below picture for detailed solution. 

Q: A stone is thrown vertically upward from the top of a house 112 feet high. If it was thrown at 96 fp...

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Q: cos2r- sin2x cos21 =-F(x)+C What is Fx)? =xp For COSX – sinư A 2. --cos 'x- cosT+-sin't 3 cos'x sinx...

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: dx - = In[F(x)]+C. What is F(/3) if C = 0? For (x+x³) (x Tan-lx+ 1)

A: Let's find. 

Q: dx -= In[F(x)]+ C. What is F(/3) if C = 0? For (x+x3) (x Tan-!x+1) -1 (A 3 3 B (c) + - 6. 1 D + -15

A: