,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

Q: If Z=x+iy and 12/=/2-81 of *= Hhe Value %3D

A: Given that       z = x+iy  and |z| = |z-8| Here we have to find the value of x .

Q: 3tan z sec? x dr 2.

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Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: If f(x,y,z)=x²y³-y²z³ Then f;= -3y²z2 Jlgn

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Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

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: ☺ cosh"z= Loy {2+/2

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Q: b) If ƒ(x,y) = 8x³y+ 3xcosy – 4y² +7e2x then verify fxy = fyx

A: We first differentiate with respect to x, then with respect to y

Q: 12. f(x, y) = x' – 2x – y + 4y, P = (1, 2). -

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Q: 4.3 Verify that for f(x, y) = 4x°y$ - 9x*y³. дх ду ду дх df

A: Explanation of the answer is as follows

Q: 4. f(x, y) = 10x²y* – 6xy2 + 10x2; fx(x, y), fy(x, y) %3D -

A: Consider the given function as fx,y=10x2y4-6xy2+10x2

Q: - a°y°, show that fæy = fyx. 85 Problem - 24: Given f(x, y) =

A: Solve the following

Q: (d) If F(x, y) = (4x² - y², -2xy), then f(x, y) =

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Q: Show that u = 3x^2y + 2x^2 - y^3- 2y^2 is a harmonic function.

A: Given: u=3x2y+2x2-y3-2y2 To show: u is a harmonic function.

Q: Sketch Z= 2x^2 + 3y^3

A: Given, Z=2x2+3y3 To find: Sketch the plot for Z

Q: f(x, y) = In(4x² - y) %3D

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Q: y show that = 0. . If z: x² + y² II

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Q: If x < 0 and y > 0, determine the sign of the realnumber. x/y

A: It is given that, x < 0 and y > 0

Q: Let f(z) = 5z2 + 3z. %3D

A: Given,            f(z)=5z2+3z and         z = 8.2+5.9i

Q: 2.,3 2) Find fx and fy if f(x, y) = 2x²y³ – 3xy² + 2x² + 3y² + 1

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Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

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Q: 3. /4(1-)esc (1-y)dy

A: We have to solve the integral

Q: 2. xy2 = 6 at point (6,1)

A: Follow the procedure given below.

Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: Find fx (x,y) and  fy (x,y).  Then find fx (2, -1) and fy(-4,3)

A: Given: f(x,y)=ln|3x4+5x2y2|∂f∂x|(2,−1)=fx(2,−1)=?∂f∂y|(−4,3)=fy(−4,3)=?

Q: Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

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Q: Show that Inx dx = -/Zn². x3/4(1+ x)

A: The given integral is: ∫0∞lnxx341+xdx

Q: س 1: أختر الاجاية الصحيحة لمجال ومدى الدالة 4 - f(x( = x2 ثم اختر الرسم البياني الصحيح؟ Dr = R & Rf…

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Q: .1//3 7earctan(y) dy + y? 3

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Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

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Q: x, prove that y¨= 2(y² +1)(3y² +1).

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Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis

A:

Q: the first dirivative of f(x) =( 5x4 - 6x)-3 will be _______

A: Given : f(x) = (5x4 - 6x)–3

Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

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Q: If x < 0 and y > 0, determine the sign of the realnumber. x2y

A: Given, The real number is x2y.

Q: 14I hox)= x)-0, whese fCn=2 and fとい=8,

A:

Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: 2. § (5z² - 7z + 3) dz from z = 2 to z = 1

A:

Q: Calculate fxyy for f(x,y) = x 3 + y2ex.

A: Given function is fx,y=x3+y2ex. To calculate: fxyy. Solution: fxyy means first partial derivative of…

Q: -2 The domain of f(x,y) = is %3D x² + y?

A: f(x,y)=-2x2+y2

Q: Express.  y=√(3x²-9)  as a composition of u(x)=√x , v(x)= (x)² , j(x)=3x-9

A:

Q: Find fx(x,y) and fy(x.y). Then, find fx(- 4, – 1) and fy(- 1,3). 23| f(x.y) = In |8 + 5x²y³|

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Q: 3 18. z= 19. y= Vx(x-1) 3x-1 20. y= 2x+1

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Q: Check whether z/z+3 is analytic or not?

A: Let     f(7)  = 77+3Now, Let f(7) = φ(7)ψ(7)where ϕ(7) ≥ 7  and ψ (7) = 7+3Here   ψ(7) has zero at 7…

Q: Use Cramer's rule to solve for y. 5x + 4y + 4z = 39 4x +3y-2z 15 4х - 5y - 4z%3D -15 |

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Q: inh´x + cosh²x = 1 = x²arccsch(x²) then f

A: 1. The function fx=y=coshx is represented as , coshx=ex+e-x2 To check whether the function is odd…

Q: If we use the secant method on fx) = x+x+3 with x2 and X-1 = 1, then X, is

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Q: Find fx ( x , y ) and fx ( 3 , -2 ) and fy ( -2 , 1 ) .  f ( x , y ) = 8xy + 4y4 + 8

A: