Determine if f (x, y) = ={(xsin3y)/(x2+y6), (x, y) ≠ (0, 0) ={1, (x, y) = (0, 0) is continuous at (0, 0)
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Determine if f (x, y) =
={(xsin3y)/(x2+y6), (x, y) ≠ (0, 0)
={1, (x, y) = (0, 0)
is continuous at (0, 0)
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Solved in 3 steps
- Find all the stationary points of the function f(x,y) = x3e-(x^2+y^2).Determine if f(x, y) is continuous at (1, 0) where (x - 1)²y² (x − 1)² + y² - 0 f(x, y) = = if (x, y) = (1,0) if (x, y) = (1,0)Determine whether the given set of functions is linearly independent or linearly dependent on the indicated interval. (a) yı = e", y2 = e-ª, and y3 sinh x for the interval (-o, ∞) (b) y1 = xe+1, y2 = (4x – 5)e", and y3 = xe" for the interval (-x, o∞)
- Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x^2 + πχ2 F(x₁ - 1) = - TUThe function f(x, y) = 2x^3 + 6xy^2 −3y^3 −150x has four stationary points, find them and classify all stationary points.Find the linearization L(x, y) of the function f(x, y) = (x^3)(y^6) at the point (-2, -2).
- Consider the following function and closed interval. f(x) = √6 - Xx, [-19, 6] Is f continuous on the closed interval [-19, 6]? Yes No If f is differentiable on the open interval (-19, 6), find f'(x). (If it is not differentiable on the open interval, enter DNE.) f'(x) = Find f(-19) and f(6). f(-19) = f(6) Find = f(b) f(a) b-a f(b) f(a) b - - a C = = for [a, b] = [-19, 6]. Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because f is not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) list. If the Mean Value Theorem cannot be applied, enter NA.) f(b) – f(a). If the Mean Value Theorem cannot be applied, explain why not. (Enter your answers as a comma-separated b-aLet f(x) = ax* + bx' + 50. Determine the values of a and b so that fx) has a point of inflection at (2, 18).3- Show that this function is differentiable for all and find its derivative f2) = f(x+ jy) = x* – 15x*y + 15x*y* - y6 + j(6x®y- 20x*y + 6xy")