Determine D„f(4, –1,6) for f(x,y,z) = ex³y + 4zx³ in the direction of (–3,2,6). %3D

Q: Estimate f(2.98, –1.99) given that f(3, –2) = 2, f«(3, –2) -3 and fy(3, –2) = -4. = f(2.98, –1.99)

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Q: Evaluate W(3,-1) for the function W(x,y) = 4x^2 + y^2

A: W(x,y) = 4x2 + y2Find W(3,-1)

Q: y®y' – 8y9 = ex ,8,

A: On simplification, we get

Q: 6 Y = x6 + Vx5 ++5 x3 y' = 6x5 +x² – 18x* y' = 6x5 +x1.5 – 18x-2 O Option 2 Option 1 y' = 6x5 +x15 –…

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Q: , (х, у) (0,0) x+y f(x.y)%3D (х, у) (0,0)

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Q: Question 3.5: Calculate o dz. Question 3.6: Calculate o 1 - dz .

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Q: b) Evaluate: i) Sx(V ++x) dx -2 10 dx ii) J1 x(10+Inx)³ jii) Jo 1+x? dx

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Q: Integrate from 0 to 2

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Q: du _ dv dy dx If f(z) =z²+z - ,2

A: Take z= X+iY and proceed

Q: ду Find ду and when dz (a) y = 6 + 3x + 16z + 4x2 + 2z2 (b) y = 14x2 (c) y = 9 + 4xz - 3x2 %3D

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Q: Suppose that I'm (f`∞x) = (x (24-1) and f(0) = 3-2i, f(1) = 6 -21, Find f(1+i)

A: Given that Imf'z=6x2y-1 To find: f(1+i).

Q: dy If y = ( a² +1) (x³ + 3) dx %3D O 5x^4 + 3x^2+ 6x 6x^3 O 2x + 3x^2 O 2x^2 +2x+ 3x^5+9x^2…

A: Question 1,Given,            y=x2+1x3+3To find: dydx

Q: Find yll of x³+y²=3 by implicit ditferetlal C1o pants

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Q: X f(x) 0,0 0,5 1,0 2,119 1,0 15 20 2,910 3945 5,72 2,5 8,695

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Q: Which of the following equation is a variable separable DE? a. (x + x^2y) dy = (2x + xy^2) dx b. (x…

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Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Solve the initial value problem y y" +2y-8y = 9 Cosx-2 sinx yea) = 4, y co) = -6

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Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: 1- x 5. dx VI - r

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Q: (3x^2+2y)dx+ 2xdy=D0, x=1, y=2 Select the correct response: NONE O x^3+2xy=5 O x^3+2xy=3 O…

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Q: Solve xy² - xy + y = 2x, xx (Cauchy-Exter; variation of parameters)

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Q: Solve the given O.D.E. by the method of "Variation of Parameters"; 1 Y" - 4 Y' + 4 Y = [12 x2 -…

A: The solution is given as