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What is the equation of the tangent plane at the point (1, 0, 0) to the surface z = ln(x² + y²)?
What is the equation of the tangent plane at the point (1, 0, 0) to the surface z = ln(x² + y²)?
What is the equation of the tangent plane at the point (1, 1, 5) to the graph of f(x, y) = x² + 2xy + 2y²?
What is the equation of the tangent plane at the point (1, 1, 5) to the graph of f(x, y) = x² + 2xy + 2y²?
What is the equation of the tangent plane at the point (x₁, y₁, z₁) to the surface z = √(xy)?
What is the equation of the tangent plane at the point (x₁, y₁, z₁) to the surface z = √(xy)?
What is the equation of the normal line to the surface f(x, y) = x² + y⁴ + e^(xy) at the point (1, 0, 2)?
What is the equation of the normal line to the surface f(x, y) = x² + y⁴ + e^(xy) at the point (1, 0, 2)?
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What is the gradient of f at the point P(2, -1) where f(x, y) = x³y + y³x - 2xy?
What is the gradient of f at the point P(2, -1) where f(x, y) = x³y + y³x - 2xy?
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What is the equation of the tangent plane to the surface f(x, y) = x / (x + y) at the point (x₀, y₀) = (1, 1)?
What is the equation of the tangent plane to the surface f(x, y) = x / (x + y) at the point (x₀, y₀) = (1, 1)?
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What is the first derivative of z with respect to t in terms of f, φ, and u?
What is the first derivative of z with respect to t in terms of f, φ, and u?
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What is the second derivative of z with respect to t in terms of f, φ, and u?
What is the second derivative of z with respect to t in terms of f, φ, and u?
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What is the directional derivative of f(x, y) = xy at (x0, y0) in the direction of (h, k) = (1, 1)?
What is the directional derivative of f(x, y) = xy at (x0, y0) in the direction of (h, k) = (1, 1)?
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What is the directional derivative of f(x, y) = 2x + y - 1 at (2, 1) in the direction of (1, 1)?
What is the directional derivative of f(x, y) = 2x + y - 1 at (2, 1) in the direction of (1, 1)?
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What is the directional derivative of g(x, y) = xe^(yx) - xy at (1, 1) in the direction of (3, 4)?
What is the directional derivative of g(x, y) = xe^(yx) - xy at (1, 1) in the direction of (3, 4)?
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What is the directional derivative of f(x, y) = x + 2x^2 - 3xy at (1, 1) in the direction of (3/5, 4/5)?
What is the directional derivative of f(x, y) = x + 2x^2 - 3xy at (1, 1) in the direction of (3/5, 4/5)?
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What is the partial derivative of 𝑥1 with respect to 𝑝1?
What is the partial derivative of 𝑥1 with respect to 𝑝1?
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What is the relationship between 𝑋1 and 𝑋2 based on the given demand functions?
What is the relationship between 𝑋1 and 𝑋2 based on the given demand functions?
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What is the partial derivative of 𝑥2 with respect to 𝑝2?
What is the partial derivative of 𝑥2 with respect to 𝑝2?
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What is the formula for the partial price elasticity of demand?
What is the formula for the partial price elasticity of demand?
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What is the demand function for 𝑥1 in the second scenario?
What is the demand function for 𝑥1 in the second scenario?
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What type of goods are 𝑋1 and 𝑋2 in the second scenario?
What type of goods are 𝑋1 and 𝑋2 in the second scenario?
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What is the condition for a function 𝑓(𝑥, 𝑦) to be homogeneous of degree 𝑟?
What is the condition for a function 𝑓(𝑥, 𝑦) to be homogeneous of degree 𝑟?
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What is the value of cross-price elasticity of good 1 with respect to the price of good 2?
What is the value of cross-price elasticity of good 1 with respect to the price of good 2?
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What is the percentage change in the quantity demanded of good 1 when the price of good 1 increases by 2% from the existing level?
What is the percentage change in the quantity demanded of good 1 when the price of good 1 increases by 2% from the existing level?
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What is the degree of homogeneity of the function 𝑧 = 𝑥 2 + 2𝑥 2 𝑦 2 + 𝑦 4 /𝑥 + 𝑦?
What is the degree of homogeneity of the function 𝑧 = 𝑥 2 + 2𝑥 2 𝑦 2 + 𝑦 4 /𝑥 + 𝑦?
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What is the value of own-price elasticity of good 2?
What is the value of own-price elasticity of good 2?
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What is the property of the first partial derivatives of a homogeneous function of degree 𝑟?
What is the property of the first partial derivatives of a homogeneous function of degree 𝑟?
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What type of goods are good 1 and good 2 based on the given demand functions?
What type of goods are good 1 and good 2 based on the given demand functions?
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What is the Euler's theorem for a homogeneous function of degree 𝑟?
What is the Euler's theorem for a homogeneous function of degree 𝑟?
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Determine the degree of homogeneity of the function 𝑧 = 2(𝑎𝑥 + 𝑏𝑦)2 - (𝑥 2 + 𝑦 2 )?
Determine the degree of homogeneity of the function 𝑧 = 2(𝑎𝑥 + 𝑏𝑦)2 - (𝑥 2 + 𝑦 2 )?
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What is the value of cross-price elasticity of good 2 with respect to the price of good 1?
What is the value of cross-price elasticity of good 2 with respect to the price of good 1?
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What is the percentage change in the quantity demanded of good 2 when the price of good 2 decreases by 2% from the existing level?
What is the percentage change in the quantity demanded of good 2 when the price of good 2 decreases by 2% from the existing level?
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What is the condition for a function 𝑓(𝑥, 𝑦) to be homogeneous of degree 0?
What is the condition for a function 𝑓(𝑥, 𝑦) to be homogeneous of degree 0?
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