O If and exist in a neighborhod of (a, b) and are continuous at (a, b) then f(x, y) is differentiable at (a, b). af af and always exist. dy lim (1,9) → (a, b) O f f(x, y) is differentiable at (a, b) then a tangent plane to f(x, y) exists at (a, b). O if f(z, y) is continuous at (a, b) then it is differentiable at (a, b). O if f(z, y) is differentiable at (a, b) then it is continuous at (a, b). f(x, y) always exists.

Q: f(z) = f(x+iy) = Z

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Q: 2. Find the tangent plane to z = x f (t) where t = at a point (a,b) not on the y-axis. [Note: be…

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Q: b) Give an example of a function g: R →R that is continuous at some xE R, but not differentiable at…

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Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x>0…

Q: A) If g'(x)>0 for all x in the interval (4,7) then g(x) is for all x on the interval (4,7).| B) If…

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Q: Find the limit 2yz lim (x,y,z) (0,0,0) x4 + y² + z² along the curve x = 2t, y = 3t², and z = 4t².

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: How would you remove the dis . z46 f(r) =

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Q: II. Analice la continuidad de la función a) f(x,y,z) = x²+3²-4 (sen (xy) xy b) f(x, y) = ,xy = 0 1,…

A: We have to check that the function is continuous.

Q: Suppose that f is differentiable on [a, b]. Prove that if f'(a)f'(b)< 0 then there exists a point c…

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Q: Let & be continuous in [a,b] and differentiable in (a,b). It's true that: a) f (a) = f(b) = 3 x €…

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Q: Assume that the functions ?,?,ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c,…

A: given: ℎ:ℝ→ℝf,g,h:R→R are differentiable such that  f′(a)=b, g′(b)=c, h′(c)=d, f(a)=e, g(e)=ℓ,…