3. Generalize the definition of gradient to differentiable real values functions of n variables for onr intogor

Q: 1-Find the gradient of (1) f (x,y)= In(x²+y²) (1,1)

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Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: Compute the derivative of f (x) = x 3/2 using the limit definition.

A: fx=x32

Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

A:

Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

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Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: f(x,y)=x² +16xy + y² +8

A:

Q: : Verify Mean value theorem for the function f(z) = 4x over the interval [0, 2].

A: As given function is: fx=4x3 Given interval is: 0,2 According to mean value theorem for a continuous…

Q: Show that f(z) = 3z2 + 2z + 5 is analytic function.

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Q: In x y = 1+ In x

A: I have written the formula used , here f'(x) and g'(x) are derivative of f(x) and g(x)…

Q: Calculate the error in using the divided differences for approximating the derivative at x 5 using a…

A: Use the Newton's divided difference interpolation formula, to obtain the equation for f(x).…

Q: B)Is w = Ze² analytical function or not?

A:

Q: First, compute the gradient of the following function. Then evaluate it at the given point F(x,y)= e…

A: gradiant of F→=∂F∂xi+∂F∂yj

Q: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

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Q: Suppose that the values of a smooth function fis known for x=0, 0.3, 0.6 and 1.2. Select the 3-…

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Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: Suppose the gradient of f (x, y) exists for all points in R2. Which ONE of these statements must be…

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Q: show steps please

A:

Q: Calculate the error in using the divided differences for approximating the derivative at x 5 using a…

A: Use the following formulae, to obtain the required result. The Newton's divided difference…

Q: Locate and classify all the critical points of the function. (If an answer does not exist, enter…

A: Topic- application of derivatives

Q: calculate the are between the curves f(x)=x^2 and g(x)=x^3 on the interval [-1,1]

A: Given,

Q: Is the function f(x)= x+|x|-1 differentiable at x=0.

A: Consider the given function:

Q: Suppose that a firm uses L as an input, and its production function changes with L and a parameter…

A: Let’s apply the above approach to an economic application, namely the profit function of a…

Q: Show that the function x² – y² 2ху f(x,y) = { x² + y² if (x,y)# 0 if (x,y) = 0 is continuous at…

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Q: B)Is w = Zez analytical function or not?

A:

Q: Show that the function defined by xy √x²+y² f(x, y) {{ = 0 if (x, y) = (0,0) is not differentiable…

A:

Q: Show analytically that the function f is not differentiable at x = 0. Ax) = 2x+1 x>1

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Q: Prove that constant function is differentiable at ever x ER.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use the Linear Approximation to estimate Af for f(x) = when a = 2 and Ax = - %3D 5+x? (Use decimal…

A: fx=115+x2,a=2;∆x=-12 Now, differentiate the function with respect to x.…

Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

A:

Q: 14. z= x- x+y

A: We have to determine gradients of the functions

Q: Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a,…

A: Find the reason why the tangents lines fit well at the inflation points

Q: Find an analytic function whose real part is e-x (xsiny+ycosy)

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Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: when that this 1x² + y² Shothathis sho (x, y) (0,0) and f(0,0) function is continous at (0,0)

A:

Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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Q: How can you sometimes decide from examining ƒx and ƒy that a function ƒ(x, y) is differentiable?…

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Q: Use linear approximation to estimate f(4.9) given that f(5) = 2 and f'(5) = 6.

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Q: Suppose f and g are two differentiable functions such that f(9(x)) = x? and supposed the equation of…

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: Show that w=f(z) =3ix+y dose not satisfy C.R.E. thus it is not analytic function

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Q: Use linear approximation to estimate f(3.85) given that f(4) = 5 and f'(4)= 6.

A: Given: - The values, f(4)=5 and f'(4)=6 To estimate: - The value of f(3.85) by using linear…

Q: If z = f(x,y) = 3x^2 - xy , get the total differentiation of z if (x,y) change from (2,3) to (2.5 ,…

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Q: The antiderivative of a given function is unique. true or false

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Q: if a set is compact set and the gradient of the function isnt equal to zero what does it mean

A: Given that the set is compact set. This mean that the function is bounded. The gradient of the…

Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: Find the linearization of f (x) = xe¯* at a = 0. (Hint: Remember thne product rule.)

A: Given : fx = xe-x2

Q: Show that the average rate of change of the linear function f(x) = a over any interval say [x1,x2]…

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Q: Show that f(z) = 3z² + 2z+5 is analytic function.

A: Given