Divergence Theorem.

Q: BA)Find normal line and parallel plane to the function f(x, y, z)=x√yz + 6 At point (-3,1,4).

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Q: Using the function what is fx and fy ? What are the critical Valves of f as ordered pairs la,y)?

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Q: If f.(a,b) = f,(a, b) = 0 then (a, b) is %3D %3D ans. critical point point of extreme isolated point…

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Q: limit.

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

A: if f is a differentiable function of x and y then function has directional derivative in the…

Q: The maximum rate of change of the function f(x, y, z) = xyz at the point (1, 2, 3) occurs in the…

A: In this question we have to find the correct answer.

Q: TRUE / FALSE) For two pdfs f(x) and g(x), f(x)g(x) is a pdf.

A: Solution

Q: (b) Apply the First Derivative Test to identify the relative extrema. (x, y) = ( ,1 2 relative…

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Q: Jeetor v makes an a with the ga

A: Given, The angle made by the vector v with a gradient of fx,y=3x2+y3-2xy at 1,1 is π6. The rate of…

Q: Autocorrelation function is maximum at the origin, i.e., |Rxx (7) |S Rxx (0) XX

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Q: (a) Find the linearization of f () = at a = 4. x+1 Enter the linearization using the equation…

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Q: 3n-4n1+1

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Q: How to check if gradient descent is diverging?

A: Gradient descent is a general-purpose algorithm that numerically finds minima of multivariable…

Q: How do you define local maxima, local minima, and saddle points for a differentiable function ƒ(x,…

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Q: What is need of divergence thoerm why we used? Give examples as well

A: The divergence theorem gives the relation between surface integral and volume integrals.

Q: Linearization approximation

A: Here, we consider the function f(x)=x^(1/3). We take x=8.5 and a=8 as, we know the cube root of 8,…

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

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Q: Find local extrema and saddle points of the function f(x, y) = y^2 - 3y cos x , -1 ≤ x ≤ 7

A: Given: fx,y=y2-3ycosx,  -1≤x≤7

Q: Ving model: Y; = Bo + B1Z¢ + B2X¢ + B3Xt-1 + B4Xt-2 + Et %3D as of freedom will vou have for this…

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Q: indicate whether the statement is true or false, and if it is false, provide a correct statement.…

A: Given: The statement "The derivatives of the cross product is the cross product of the derivatives."…

Q: Using an appropriate linearization, the local linear approximation o

A: Recall the local linear approximation formula:

Q: continuous function h(x),

A: Differential equation

Q: Searches related to the height of a plane is the function of the time since take off. Identify the…

A: Given that:   The height of a plane is the function of time since take off.

Q: Prove of divergence in detail please.

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Q: -, 0) ; absolute minimum point at the point (-3, rema. e point (-4, 0) ; absolute and relative…

A: We have to choose the correct answer from the given options according to the given information

Q: Is the average rate of change of a function between x = a and x = b the slope of the secant line…

A: Average rate of change of a function between x = a and x = b the slope of the secant line through…

Q: (a) Show that a differentiable function f decreases most rapidly at x in the direction opposite the…

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Q: Examine the function for relative extrema and saddle points h(x,y) = (x² + y²) + 2 %3D

A: Given function is h(x,y)=(x2+y2)1/3 + 2 We will calculate relative extrema and saddle points of this…

Q: The exponential map ex

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Q: Locate all relative extrema and saddle point(s) of f(x, y)= 2x?y-x² - y².

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Q: Classify the point (1, 1) for f(z, y) = zye" 2 by using Second derivative test if POSSIBLE. Lütfen…

A: Given that,                  fx,y = xye-x2-y22 . We have to classify the point 1 , 1 for fx,y by…

Q: Consider the function f=x². Assume that the learning rate a= 0.1 and the initial value is x=2. Using…

A: To find minimum of a function we can use  gradient descent of a function at any point, which…

Q: Orthogonal Trajectory of the Curve x2+y2 = 2 In Cx

A: From the given curve; x2+y2=2lncx Now differentiate with respect to x. So,…

Q: Find the local maximum and minimum values and saddle points, if any of the function S(r. y) =+ y' –…

A: Second Derivative Test :

Q: Examine the function for relative extrema. (If an answer does not exist, enter DNE.) f(x, у) %3 2x2…

A: As per the company guidelines we are supposed to solve only first question or first 3 subparts in a…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: divergence and curl of F.

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Q: ostic plot from a linear least s x

A: Here we have given plot of standardized residuals against explanatory variable it is helpful in…

Q: Transformation Rule: (x ,y )-_

A: Reflection along line x=-2 will have follwing change :   Y coordinate will be same as earlier. X…

Q: Fitting of Gompertz curve.

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Q: Fundamental Theorem: Let f(x) = [ Jcos (In t)dt . Find the value of f'(æ). %3D

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Q: Find the linearization of f(x, y, z) = 2 centered at (1,3, 2). Use it to estimate f(1.01,3.01,…

A: Given:fx,y,z=xyzTo find a)The linearization of f centered at 1,3,2b) use a to estimate…

Q: Question Find all the critical points of and classify them using the second derivative test. f(z, v)…

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Q: Draw a simple sketch of direction field for y' x2 – y2. Find all equilibrium points and the regions…

A: The sketch of direction field is as follows

Q: joint pdf of two randor f(x, y) =

A: Note: As the question contains more than 3 subparts, first 3 questions will be solved. Please…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.