1 V1 – x z 1 – at x = 0 x, 2

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: 2: find fr. fy, and fz. a f(x, y. 2) = I+ xy- 22 2

A: Given f(x,y,z)=1+xy2-2z2 To find fx, fy, fz

Q: Dy + y Prove that is equivalent to 1 for x 0. 16x

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Q: 1. Evaluate f[x(1-x*y² +xy )dydx. 01

A: To find the double integration

Q: 1. Find D„f at P: f(x,y) = sin(8x – 5y); P (5,8)); u=((i)

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Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

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

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

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Q: 2. f(t) = e-at sin w tu(t) 3s+4 6. s2+9

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Q: Find the absolute maximum and minimum of f(x, y) = 4x2 + 2xy 3y2 on the unit square 0 sx s1, 0 sy…

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Q: If F (x)= [V5t² – 3t dt find F'(3). a) 0 b) Viz c) d) 3 e)

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Q: 7. Let f(x, y) = 10xy* + x°y². Find fyyy. 4

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Q: Find a point zo where the function f (z) = (z – 12 – 12i) (z – 12 – 12i) is differentiable. What is…

A: Given f(z) = (z-12-12i)(z -12 -12i)¯

Q: Verify the final value theorem of f(t) =1+et[sint + cost]. O- 1 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 a point zo where the function f (z) = (z – 8 – 6i) (z – 8 – 6i) is differentiable. What is the…

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Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

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

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Q: express in the form y = f (x) by eliminating the parameter  x = t 2, y = t 3 + 1

A: Given, parametric equation is:  x=t2,y=t3+1 Solution: x=t2,⇒t=±x     ...(1)y=t3+1 ⇒y=(±x)3+1…

Q: 8. Find the work done by F = (x² – y,x) along C:7(t)=(2cost,2sint) 0<t<2n : a) Without Green's…

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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: Calculate the LOS of y = x² LOS is x = a is b is c is

A: Given equation is in the form of ax^2+bx+c=y Here a=1 b=0 C=0.

Q: Find the Complete or Particular solution OF the Followoilng diffi rential equations: (2メコ+ )dx -2メよ…

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Q: Find T3 centered at x = a. 1. f(x) =e2x,a = 0

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Q: Given f(x, y) = 2e" sin(4y) v (0, then V %3D 2

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

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Q: wherey = x + C is a solution to this DE. What is the particular solution?

A: Let's find.

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

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Q: Q1: Use Green's theorem to evalute f. (xy + y2)dx + x²dy by the curve y = x and y = x2.

A: Given problem:- Use Green's theorem to evaluate ∫c (xy + y2 )dx + x²dy  by the curve y = x and y =…

Q: Solve for y(t) where y(t) + 2 / a – u)y[w)du = t.

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Q: 19 Suppose that Ts Cx) centered at 2 for f (x) is gicn by Ts Ca):345Ca-2)+5 Cx-2)?ょ2x-2)+(x-2) Than,…

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Q: Q3) for f(t) = sec²(6t – 1) and g(t) = tan?(6t – 1) show that %3D %3D f'(t) = g'(t). %3D

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Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: s zy dydz こミ0

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Q: Let f(x, y) = /T²(1 – y²). Find fr (0, 1).

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

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Q: Find the linear approximation at x=0 to √17−x. Write your answer in the form y=Ax+B.

A: we have f(x)=17-xDifferentiating both side w.r.t "x"f'(x)=-1217-x-12f'(x)=-1217-xput x=0f'(0)=-1217…

Q: that is tompent ☺ Find the equation to the the Cime curve of fG)= (4-3)9 at x =l 4 (Tes f(x) =…

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Find dr dy at x = -1 if y =u° +5u – 4 and u = x² +x.

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Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

Q: Find the G.S. about xo = 0 for: (x² + 4)y" + xy = x + 2

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Q: Find T3 centered at x = a. 1. f(x) = 1 a = –1 2+x

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Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

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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: 0If z-x"f), show that xZ+JZy=mZ.

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Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

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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Q: Please solve the Vƒ of the function below at point P. a) f = (x² + y² + 2)-05, P; (12,0, 16) b) f =…

A: a) The given function is f=x2+y2+z2-0.5. This gives ∂f∂x=-0.5 x2+y2+z2-0.5-1…