4. a) Find an approximation for f (x, y) = at the point (1.97,1.02). V10-r-5y b) Check Euler's theorem for f(x, y) = x – y5x + x³y³ .

Q: consider a function f, defined by f(x,y) = -y/√x2+y2   what is the behavior of f along the line…

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Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

Q: (x, y, z) = 2x²y — xz² + 3y²z. Xyx

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Q: What curve is described by the function (t) = (2t + 3) + i(t - 5), 0 ≤ t ≤ 1

A: Step:-1 Given parametric function is ft =2t +3 +i t-5,  0≤t≤1 Here,  x=2t +3  ---(1)y=t-5  ---(2)…

Q: Derivative of y = 16 is: a) 1 b) 0 Derivative of f(x) = - 6x + 2 is: a) - 4 b) 2 Derivative of g(x)…

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Q: √x² + y² x-1 (a) Find and sketch the domain of f (x, y). 2. Consider the function f (x, y) = 4 (b)…

A: The given function is  f(x,y)= x2 +y2-4x-1 We know that the domain of a function is the set of…

Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: valuate f (z) dz.where C is the parabola y =x2 from z =-1+i ti 7 = 1+i and S (z ) = 6.x

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Q: For the given function 9 = x-yz and 62 -(@C) at C= 3x?yi+ yz²j- xzk, Find 5yöz бубz point (1, – 2, –…

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Q.3) Find the constants a, b, c, d, e if f(z) = (ax³ + bxy² + 3x² + cy² + x) + i(dx²y - 2y³ +exy +…

A: Given :  f(z) = ax3+bxy2+3x2+cy2+x + idx2y-2y3+exy+y  is analytic. To find : The constants a, b, c,…

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: Find the equation of the tangent plane to the graph of 7y √x f(x, y) = at the point (9,-1). (Use…

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: the doi n ain of the functions

A: We have given two functions : f(x,y)=1xy…

Q: B. Find and classify the extreme points of function f(x, y) = x + y - 4xy-1.

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Q: a) Find the domain and range of the function f(r, y) = Vy – 4+ SUTM 1 UTM x2.

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Q: Show that f xy = f yx for the following function: (x1² y) f(x, y) = 24 + In(x1² + y36 )

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Q: Find m such that the function y= Aex satisfies the equation 2y"=y'+y

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Q: Let x + y = 28. Find y"(x) at the point (3, 1). "(3) =

A: The solution of the problem is given in the next steps.