04 Let f(x, y) = x² + y². Which one of the following is the minimum directional derivative of the function f(x, y) at the point (x, y) = (1, 1)? -sqrt(8) sqrt(8) -sqrt(2) sqrt(2)

Q: et Evaluate the derivative: da 4 S (3t2 – 2t + 4) dæ.

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Q: Find an equation of the tangent line to the curve at the given point. y = In(x2 - 8x + 1), (8, 0) y…

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Q: (8) Given x²/3-y²/3 - y = 3, find ae equation of the tangent line at the point (1,-1).

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Q: 3) Show that the function 13-212+2 g(2) = is a Complex differontiable function ait the point 20 =1…

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Q: Let M (2,1,3) and N(5,5,15) be two points. Find the derivative of the function f (x, y, z) = xy + yz…

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Q: Part 1 a) Given f (z) = + x2 + i(2x2 - y?), show which points where f has y a derivative. b) Show…

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Q: Determine whether the equation defines y as a linear function of x. If so, write it in the for…

A: For the given function, 2√x +3y= 0 3y= -2√x y= -(2/3)*√x So y is not a linear function of x.  Option…

Q: Find the maximal directional derivative of function f(x,y) = xln(x+y)+x²y at the point (-1,2).…

A: To find -

Q: of and ду of Consider the function f(x,y) = 9x' - 4y - 2. Find -

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Q: - Find and sketch the domain of the functions: √x+y+1 x-1 b) f(x, y) = x ln(y² - x) c) f(x, y) =…

A: The given functions, a) fx,y=x+y+1x-1b) fx,y=xlny2-xc) fx,y=6-3x-2y We have to find the domain of…

Q: A function f of two variables has a function equation of the form f(x, y) = ln(ax²y + bxy + c) where…

A: Given that the tangent plane to the function f(x,y)=ln⁡(ax2y+bxy+c) is z=−6x−y−3 at the point…

Q: For the function f(x,y) = sin (3x − 7y), find of of dy of af and ?x ду

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Q: Let z be a differentiable function of z and y related by the following equation: 1+1=(√y+cosh(z)) ².…

A: Given: The equaiton is x+zx-z=y+coshz32. To find: The value of ∂z∂y at the point 3,0,0.

Q: 3. Let f(x) = 2x - x². (a) Find the secant line to the graph of f passing through the points (0,0)…

A: We can find equation of secant line and tangent line .

Q: the contour diagram of o decide if the specified directional derivative is positive, negative,…

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Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: Let z be a differentiable function of x and y related by the following equation: x + ² =(√y +…

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Q: d (a) / ₁ (t²-1)²dt. -10 -10 (b)/(t²-1)²dt. (c) d dx 32² -10 3x² (t²-1)² dt. d (d) — (t²-1)²dt. dx…

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Q: Let f : D → E be a function and let A C D, BC E. Prove the following: (a) f(f-1(B)) C B. (b) If f is…

A: The function is f:D→Eand A⊆D and B⊆E

Q: 1. Let F(x, y, z)=x²+4x2+2yz². What is the direction of fastest decrease of Fat (1,2,-1)? (a) (b)…

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Q: 9. f'(x) = 4x³ + 5x² – 7; f(0) = -3

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