Let f(x, y): = lim (x,y) →(0,0) (x,y)=S₁ O 0 O 6|5 312 3 say x² + y². f(x, y) = If S₁ is the set of points along the line y = 2x, then

Q: Examine the continuity of f(z) = 2-√z+4 Z at z = 0

A: Given: fz=2-z+4z We have to find the continuity of f(z) at z=0.

Q: Let X {1,2, 3} and Y {3,4}. Define f : X → Y as follows: = f(2) = 3 and f(3) = 4. Draw an arrow…

A: We will draw the arrow diagram for function mapping from set A to set B.

Q: Sketch a contour map for f(z. y) using the k-values, k = 1, 2, 3. |f(x, y) = |x| + sin(y)

A: Given : f(x,y)=|x|+sin(y)   To sketch : contour using the k-values k=1,2,3

Q: 21. Let f(x) = 2x, x = [0, 1]. Take P = {0, 1, 1, 1, 1, 1} and set x₁=1, x₂ = 16, x3 = 3, x4={, x3 =…

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Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2rs, s² - 6r). Use the table of…

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Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

Q: f(x, y) = /36 – x² – y², then the level curve f(x, y) = 7 is empty. - ect one: True False

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 3. Let f: R³ R be defined by f(x, y, z) =|| x ||. Find Vf(x, y, z). What is the domain of Vf?

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Q: Let f(x) be a function; then which of the below item/s can hold? (you can choose more than 1 item)…

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Q: Which one of the following relations is not a function? O ((x.y): r, y ER and r + y² = 1) O ((x.y):…

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Q: Let f (x, y) = e3x-49). Find the equation for the tangent plane to the graph of f at the point…

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Q: Show that F is conservative and find a function f such that F= Vf, and use this result to evaluate F…

A: Given  F→x,y=6x2y2−8xy3i+4x3y−12x2y2j and A1,2 , B2,2 Let M=6x2y2−8xy3 and N=4x3y−12x2y2…

Q: g4 – 2y² f (x, y) as (x, y) → (0,0 x2 + y2

A: Given that: f(x, y)=x4-2y2x2+y2

Q: Show that the segment of the tangent to the a+√√a²-x² 2 -√a²-x² contained betw 2 a-√√a²-x² y-axis…

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Q: Let f(x) = |x|+|x−2], x € R. Find points where f is not differentiable.

A:

Q: tch the following contour diagrams (cross-sections to the z-axis) to the following fund II) IV) 0.5…

A: Given contour diagrams and their functions. The objective is to match the contour diagrams with…

Q: Suppose f is a differentiable function of x and y, and g(r, s) = f(2r – s, s - 3r). Use the table of…

A:

Q: there are three variables X Y&Z denoting GDP, fiscal expenditure and fiscal revenue. which of the…

A: The possible is cov(x,y)= 356 because covariance can be any value between negative infinity to…

Q: Find the length of the line given by r(t) = ⟨t, 2t⟩, for a ≤ t ≤ b.

A: To determine: The length of the line given by rt=<t,2t> for a≤t≤b

Q: 2. Let f= L(X,Y). Show that ƒ is one to one iff (f(x).(x)....(x)) is linear independent when (x,x)…

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Q: 3x3+y² x²+y² .2 (x, y) ± (0; 0), ,2 ) f (x, y) = 1, (x, y) = (0; 0).

A:

Q: \lim_{x\rightarrow 7}\frac{x^2-5x-24}{x^2-4x-32}x→7lim​x2−4x−32x2−5x−24​

A: find out the limits of  a)limx→7 x2-5x-24x2-4x-32 b)limx→7x2-4x-32x2-5x-24

Q: Let f(x, y) = x2 − 2y and g(x, y) = xey . Show that at any point (x0, y0), the level curve of f…

A: To show that at any point the level curve of f and g intersects perpendicular, it is enough to show…

Q: 2. Given f (x, y) = x + 2y, find F(x, y) =Vf and sketch it along with the contour map of f.

A:

Q: Let z = V162 – 4x? – 9y?. (a) Find the domain of f(x, y) in R?. (b) Sketch the contour map of f(x,…

A: Domain: The domain of a function z=fx, y of two variables is the set of those points  x, y in the…

Q: of the following statements I. Let f and g be continuous real variable functions defined over the…

A: