the extremum of f(x,y) = 7x²y² +5y² 9x?. +

Q: Compute dy and ∆y for y = sqrt(x^3 + 1) for the change in x from x = 2 to x = 2.03. Is dy a good…

A: According to the given information, it is required to determine dy and Δ(y) for the given function…

Q: Suppose f(0.25)=f(0.75)=b. If the Composite Trapezoidal rule with n=2 gives the value 4 for \int_0^1…

A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

Q: Let f(x, y) = 12x² + 7y² + 3x + 3y+ 6 Find D = frz · fy – fåy-

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: ven f(x,y) = -2xy² where x = 5t and y = 8t2. Findf' (t) at t = 3. %3D

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Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

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Q: Integrate f(æ, y) = e2=² + 2y² over the domain {(x, y) | æ² + y? < 3}

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Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: Find the absolute maxlimum of frr.y)=xy subject to the Coustraint glxy)= x²ty²=/

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Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(x+y) * (xy-1).

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Q: express in the form y = f (x) by eliminating the parameter x = t + 3, y = 4t

A: The given parameters are x=t+3, y=4t. The objective is to express in the form y=fx by eliminating…

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: If y = f(x) is the solution of (5aty – 12a – 2y³)dx + (x³ + 4y³ – 6xy?)dy = 0, f(0) = 0, then

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Q: A particle is moved along the x-axis by a force F(x) = x² + 5x – 6 . How much work is done in moving…

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Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: dz dz and of the function xsin(y+ z) – xy + z² = 2y. ду -. Find the əx

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Q: <plain why y = t² – sin? t cannot be a solution to y" + p(t)y' + q(t)y = 0 nere and q are both…

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Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: Find the quadratic approximation at (0,0) for f(x,y) = e^(xe^y) .

A: Solution:

Q: Find fr and fy- f (x, y): 6e dt 4 fa(x, y) = fy(x, y) =

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Q: 2 5. x = 1+t2 2 y= t(1+t?)

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Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: ||| V3(x² + y²)dV, where V is bounded by y = 2x² + 2z² and y = 8.

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Q: Show that 3x f(x, y) = (5x³ – 4y³)ey + 4xy? is homogeneous.

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Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: Find a continuous solution satisfying dy dx + 2xy = f(x) where { x if 0 < x < 1 romer 0 if x ≥ 1 ,…

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Q: If y = x(x – 1)* then y' at z = 2 is equal to

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Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: Let ulx) be the solution of the IuP xy'-2y:x, yQ)=0 Evaluate y(32) %3D

A: In the question we have to find y(32).

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: At what interval is y=2x4- 4x2 concave downward? Ux> 3 3 3 3 V3 3 <x< 3 3 <x< V

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Q: 8) Confirm that the stated formula is the linear approximation at x =0 %3D (1+x) =1+15x

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Q: x² + 5x ,14.f(c) = = 14 f(x) on interval %3D %3D x - 1

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Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: At what interval is y=2r4- 4x2 concave upward? U x> 3 x 3 3 <x<- 3 3

A: The given function is y=2 x4-4 x2 We have to find the interval at which the function is concave…

Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

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Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

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Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: Find the local extremum of the function • f(x,y) = xy² – 6x² – 3y²

A: Find the local extremum of the function f(x,y) = xy2 - 6x2 - 3y2

Q: 1 V1 – x z 1 – at x = 0 x, 2

A: Since you are asking part (c). We are answering only the (c) part for you.…

Q: Find a function f:R² → R, its tangent plane at the point (1; 1; f(1; 1)) is given by -2x – 9y – z+8…

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