for the function given:  a) Show that the function has any vector derivative in the direction of the unit vector u = u1i + u2j at the point (0, 0). b) Is the function continuous at the point (0, 0)?

Q: Consider the function Question 1 x f(x, y) = -y ln x + x lny + y a) Find the directional derivative…

A: Hints: The given function is f(x,y)=-ylnx+xlny+xy The direction vector of a is a⇀a. Therefore the…

Q: Compute the derivative of the vector-valued function r(t)=⟨sin2t,et2⟩.

A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

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Q: a) Find the directional derivative of the function f(x, y, z)= x² y2 (2z+1)2 at the point P:(1, - 1,…

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Q: Given the following relation between x and y answer the following questions. a) Using implicit…

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Q: Suppose that f(z,y) is differentiable, and suppose that the directional derivative of f at the…

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Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a>0 and it's constant here we have to see the effect of b so,…

Q: Let r(t) be a vector-valued function such that the magnitude of r(t) does not change over time. Use…

A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: find the directional derivative of the function in the direction of the vector u = cos i + sin j

A: Consider the given function, fx,y=sin2x+y Here we need to find the directional derivative of the…

Q: 2. Consider the function f(x, y) = a) Find the directional derivative of f in the direction of the…

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Q: (- 4,3). a) Let f(x, y)= x²y°. Find the directional derivative of f at P(-1,1) in the direction of ū…

A: a)

Q: Suppose that the directional derivative of a function f at a point P in the direction of the vector…

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

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…