Consider that y is a function of x, then (x – h)? + y² = r² where r is a parameter. %3D -

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Q: yyx² +y? F(x,y) = - is a homogeneous function of degree

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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: Consider the function f (x, y, z) = x² + y – xyz Find grad

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Q: Find the linear approximation at x = 0 to Write %3D 2- your answer in the form y = Ax + B. %3D

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Q: Let y = f(x) be a derivable function implicitly defined by the equation x2 + y2 = 1 . Calculate y'.

A: The power rule of differentiation to differentiate a function of the form y=xn,is stated as…

Q: Find all stationary points of the function z = f(x, y) = 3x² – 6xy + 2y³.

A: To find stationary points of the function z=fx,y=3x2-6xy+2y3

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A: To find  f(x)=x|x| is differentiable function or not.

Q: integrate the function f(x,y) = x^2 +y^2 over the unit circle

A: In this question we  integrate the function f(x,y)=x2+y2 over the unit circle the unit circle…

Q: Differentiate the function. y = In(e * + xe) + xe¯x y' = %3D

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Q: f(x, y) = x² – y²

A: f(x,y) = x2 - y2 Let us firstly find the first order partial derivatives of the given function.…

Q: Assume that y is a function of x. Find (d2y)/(dx2) for x2y-y2-2(sqrt x)+4=0 at point (1,2) 7/6 8/6…

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Q: H.W: Find the domain of the functions f(x.y): xy g(x, y. ) : %3D -

A: We will find the domain of the Functions  Domain :- The domain of a function is the set of all…

Q: S(x,y) =-x' +2x*y-² -4y+12 ED CALC

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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 the direction in which the given function is increasing most rapidly at the point P, (-2, –1,…

A: Given function f(x, y, z) = x√(y² + z²) We have find the direction in which the given function is…

Q: Parameterize the given curve. (x + 9)2 + (y – 4)² = 4 %3D c(t) =

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Q: Find a linear approximation to the function f(x,y) at the indicated point. 2x°y f(x,y) = at (5,1) 1…

A: Linear approximation to the function f(x ,y) at (a, b) :       L(x ,y) = f(a ,b) +(x-a) f x (a, b) +…

Q: dy -from the function y= sint, x= cost as a parameter. da? Obtain

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Q: Show that the Cobb-Douglas function F(x, y) = bx" y" satisfies the equation ƏF ƏF + y (n + m)F(x, y)…

A: Given that the Cobb-Douglas function F(x,y)=bxnym We have to satisfies the equation…

Q: If a function y = f(x) satisfies = y, %3D then %3D dr y = e".

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Q: Show that the function f(x, y) = (y + ax)?e+ax satisfies the equation given by ах dy?

A: It is partial derivative problem

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A: z=x+xsiny+xy

Q: ,use the linearity of L   determine L[f]. Q. f(t)=cosh bt, where b is constant

A: Given,

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Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: (s) Find and sketch the domain of the function. (a) f(x, y) = Va2 + y², z < 4 (b) f(x, y) = V1– x² –…

A: Given that f(x,y)=x2+y2 , z≤4x2+y2 ≤4Domain (x,y) ∈R2x2+y2 ≤16The closed disc centered at (0,0) with…

Q: Find Greens function for: d?y – a²y = f(x) dx? where a is a constant subject to boundaries: y(0) =…

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Q: a) Find the linearization of the function f (x) = Vx at a = 9. %3D %3D b) Use part a) to approximate…

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Q: (e) Find and classify the stationary points of f(x, y) = x³ – 6xy + 8y³. %3D

A: Solution   c f(x,y)=x3-6xy+8y3       first we write down the partial derivative of f(x,y)…

Q: Consider the function f(x, y) = Va+y+I x-1

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Q: Give an example of a linear function f(x)= mx + b, with m,b ±0 and an interval a<xsc where f(x)dx=0…

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Q: Given the equation x + 4xy + y* = 8, evaluate dy Assume that the equation implicitly defines y as a…

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Q: dy Given the equation x? + 4xy +y° = 8, evaluate Assume that the equation implicitly defines y as a…

A: Given query is to find derivative of the given expression with respect to x.

Q: Consider the function f(x, t) = (x – ct)° + (x + ct)° where c is a constant. Calculate and dx2

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Q: Given the equation y In (x+y +6) 36, evaluate Assume that the equation implicitly defines y as a…

A: The equation is given by y lnx2+y4+6 = 6…

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Q: Find when z% = xy, where x = f(t) and y = g(t) %3D

A: Given that z=xy2, x=ft and y=gt find ∂z∂t

Q: Find the linear approximation to the equation f(x, y) = 2, at the point (4,6,4), and use it to %3D…

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Q: For which values of a e R is the function ++(). f(a + iy) = (a²z - ary) + i + ay an entire function?

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Q: Consider the function f: R²R given by f(x, y) = ³ + ² + 2xy + y2-y. Find and classify all stationary…

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Q: find the extrema for f(x,y)= x^3 +y^3 -6xy

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Q: Find the extrema of the function f (r, y) = y(x² + (In y)²), y > 0.

A: Second derivative test of two variable  function is Da,b=fxxa,b×fyya,b-fxya,b Then  If Da,b&lt;0,…