1. Given f(x, y) = x' + y* find and ax?' dy' axðy дудх 2. Find whether the function F = (r² – y' )i + (v² – 3x )j + ( - xy ) is irrotational. 123 SSS»vz (r² + y² + z* }trdydz ryz 3. Evaluate the integral 000

Q: Evalule the following" SS ye-xY dA, R - [y 12, 13] *[11, 2]

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Q: Find order and degree of y'+ (y")? =(x+y")? O a. 2,1 O b. 1,2 О с. 1,1 O d. 2 ,2

A: The given differential equation is                                              y'+(y'')2=(x+y'')2…

Q: 11. Integrate the function. y? -dy (49 – y² ) 5 y 7y +C - sin"' y + C V49 – y V49 – y² V49 - y -…

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Q: el For the function z = f(x,y) = - 4x³ -6y² - 7xy, find t V ne ON dz dx dz 3x forr || f(-5,4)=…

A: The given function is: z=fx,y=-4x3-6y2-7xy   As we know that; The Power Law: ddxxn=nxn-1

Q: x3 dx (x – 1)5 y = Select one:

A: First evaluate the integral by substitute method. Then apply the limits of integral.

Q: a) f„(x, y) b) f (х, у) уу ух 1 3 Зу'х + 5ху 3y'x .3. f (x, у) 16x*y4 -

A: (a)

Q: transcribe the following text in digital format

A: Note: "As per your requirement the given below answer is in digital format".

Q: f(x,y)=arcsin( x² +y² –1)+Jx² +y² -1 %3D

A: Definition set of the function is the interval in which the function is defined We know that Domain…

Q: 13. Find mzEDC. (9x- 1)° EE C. A (2r + 13) D

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Q: 9. What is the domain of the function f(x) = Vx- 3? | A. (3, 0) B. (-00, 3] С. [3, о) D. (-00, 3)

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Q: Find the domain of the function f(x, y) : Vx2 + 8y2 – 5.

A: follow next step

Q: 15. /7.- dt 16. x+ 3 dx P + f - 21 2r - &r

A: Solution:Given      ∫dtt3+t2-2tFormula:∫dxx=log x+C

Q: Determine the interval where b must belong so that the function f(x,y)=x^(2)+bxy+y^(2)−b^(2)x−2by…

A: We are given, f(x,y)=x2+bxy+y2-b2y-2by..............(1) and x2+y2<925................(2) We need…

Q: 1. Consider the function y = f(x) displayed below. y 3 это 5 (a) For which values of x in the open…

A: Let's analyze the function y = f(x) displayed in the graph and address each part of the question:(a)…

Q: Given a function f(x,y,z) = (x+10) In (5y - 6) sin (5z). Find the domain of the function.

A: To find domain of function

Q: y=f(x)=x' - 4x +10 find the interval that f(x) graph is concave down. O A) (2, infinite) O B) (0, 3)…

A: Given that the function y=f(x)=x4-4x3+10 Find the interval such that graph of the given function is…

Q: af ?x of ду = = af * \f f(x, y) = C(xy)", with \xy| < 1, find and af = : ду n=0 #

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Q: When z = f(x,y), which of the following is true for the whole statement? O ddz = f"(x).dx² and dx2…

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Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: Q1. Let f(x, y) = x²y + x + y² +3. (a). Find f(x, y). (b). Find dy

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Q: dr 19. 1/2 23 de 21. (2-z 2) dr 22. t 1/2 dt 27 t +1 dt 23.

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Q: f(x,y) af ?x af ду = af ду X 2x² + 8y² f(x, y) = tan af ?x (5)

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Q: 'on the interval (0, 2 7) 27. Determine the relative extrema of the function y =2cosx+sin(2x). 5n…

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Q: .. Find the absolute extrema of the function with its corresponding constrain. a) f(x, y) = x² - y²;…

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Q: Find the values of a and b so that f will be differentiable at x = 3.

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Q: дхду дхдудх dx² dy

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Q: f (x,y) =x³ cos y Given df (2, 1) дх of and (2, л). Evaluate ду

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Q: xye-(2²+v°+z*). Find all points (x, y, z) such that Vf(x,y, z) : Question 2. Consider the function…

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Q: tion 16 of 17 Let P be the tangent plane to the graph of g(x, y) = 18 – 9x - 18y at the point (4,…

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