b f (x) = Tx2 - a² R\{a,-a} R\{a²,-a²} R\{a²}

Q: - f(x, y) = Vx5 + y5. Find f-(0, 0).

A: Given that fx,y=x5+y55.It is required to find fx0,0.

Q: 2. F(x, у) %3D — (у i-2x) y2

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

Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

A:

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: -f(x) = x* – 6x³ –+ Vz7 %3D f'(x) = %3D id x5

A: Given,            f(x) =72x4 - 6x3 -2x5+x73

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

A: Solve the following

Q: If f(x,y)=xe"*/2+135x?y3, then əx²əy³ at (1,1) is equal to

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Q: f(x,y)=x² +y° +3xr² – 3y² –8

A: Given f(x,y)=x3+y3+3x2-3y2-8To find critical points, we first compute∂f∂x and ∂f∂y  ,…

Q: Find y' by implicit dif ferentiation for 2y³+4x² –y = x6 . 6x5- 8x y '=- 6y2 – 1 A 6r5 + 8x B 6y2– 1…

A: Given, 2y3+4x2-y =x6 We have to find y' by using the implicit differentiation.

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

A:

Q: If f (x, y) = x(x² + y²)-3/2 esin(a²y) find fa(1,0).

A:

Q: If SeF dr = [c(-5x + 3y² ) dx + (x³y) dy, what is F? %3D F =

A:

Q: If f(x) = S5 (t³ + 7t² + 3) dt then f"(2) =O

A: To find the second order derivative , we first invoke the fundamental theorem of calculus , which…

Q: 2 + x², -2 < x < 0 f(x)dx; f(x) TX + 2, 0<x<4 21 -2

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Q: f (x, y) = x+ 5y 2 +y = 25,

A:

Q: -x-1 a) y' = +2yi-1 v(0)=1

A:

Q: [x² - y² If f(x,y)=2x-2y m if y = x if y=x then:

A: Given the function,   fx,y=x4-y42x-2yif y≠xmif y=x

Q: Evaluate f Vx² + 4ax + a² dx :- 2a Vx2 + 4ax + a² 3a? * In x + 2a + Va² + 4ax + a²|+C - z+2a /æ² +…

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Q: Se-2t if 0 3,

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Q: Find fxy(x,y) if f(x,y) = (x² + y²)6.

A:

Q: f(x,y)=(3x^2+3y^2)

A: Given, f(x, y)=3x2+3y2 BOUNDARY OF A DOMAIN :- It is the set of all boundary points of the domain D.

Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

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Q: 6x + 17y df f f(x,y) then i : 6x 17y ду 204x (6а — 17у)? - 204x - (бх — 17у)? 204x (6x + 17y)² 204x…

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Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

A:

Q: f(x.y) = 4x - 8x + 5y² + 6; R= {(x.y)(x= 1)² +y² s1}

A:

Q: f(x,y) = x +y +8x- 2y

A:

Q: If f(æ) = (t3 + 2t2 + 5), dt then f'"(x) %3D

A:

Q: The antiderivative of the function f(x) : .2 + 11x³ is, 4 - + 2.8x4 + c - -11 + 1.2x* + c -5 + 2.8x…

A: As we know that if we need to find the antiderivative of f(x);   So,   ∫fxdx=Fx+C   From the given…

Q: If f(x, y) = (y² + 2xy)x² then fxxx equals: A) 8y O B) 12y O C) 16y O

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Q: f: Z→ No, x→ 2x, -2x - 1, when falls x ≥ 0 falls x < 0 مید ماس

A:

Q: R ,,D المناسبة ل لداله الاتية : س / أختار قيمة x-2 f(x) = x+2

A: Root of the function is 2.

Q: S2-3x', x>2 Vx -2, х <2 а) g(x)-

A: The given function is gx=2-3x3,   x&gt;2x-2,    x≤2. Sketch the graph of this function as shown…

Q: a.f(x, y) = (x² +x + 1)e¬r²/10-y²

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Q: f (z) = VE g (z) = V5x - 4 %3D

A:

Q: f(x, y) =x2 +4y3, x2+ 2y2 =2

A:

Q: The antiderivative of the function f(x) 6 + 8x is -8 + 3.0x2 + 6 + 4.0x2 + c 6 + 16.0x? + c -6 4.0x?…

A:

Q: Consider F = (4x°y+0, 9x³ + 5y+). Then div(F) = Aæ²y!0 + By³. What is the value of B?

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Q: 19 -e 8x + · -2x y = c¡e¬* + c2e¯ xe8x %3D 8100 90

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Q: Find the value of x and y for f(x)=3x2+9xy-y2-9x,if fx(x,y)=0 and fy(x,y)=0

A:

Q: If f(x) | (* + 7t² + 6)dt then f''(x) = %3D

A: f(x)=∫0x(t3+7t2+6) dt

Q: f(x,y) = x² - xy +y² – 9x + 6y + 10

A:

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7.

A:

Q: f (x, y) x+ 3 ху 3 Бъ-х

A:

Q: If f(x) = |, (t3 + 4t2 + 7) dt then f"(x) = ||

A:

Q: Use the characteristics method to solve the problem U, +3yU, = 2U , U(x,1) = f(1+ x,)

A:

Q: (x = s² – t² y = s·t³ z = 2x – 5y,

A: See the attachment

Q: ax+b 35. у%3D cx+d 36. y= (x'+4x) 1) 37. y (r-x+ 38. y = V1+2x+x 39. y= (1+x*)" (1 +x* 40. у%3 (r*…

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Q: f(x,y) = 3y3 – 2xy + 12y – 3x² – 8x – 16 then fy equals ух

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Q: f(x) = { Sx + 2 1-x+3 x>-2 Dano

A:

Q: Suppose that f(r, y) = x² – xy + y² – 4x + 4y with – 4 < x, y < 4. -

A: 1.)  Given Function is  f(x,y) =x2-xy+y2-4x+4y  with  -4≤x,y≤4  Then, fxx,y=2x-y-4…