5. Show that the function h(r, y) defined by if + y <1 h(r, y) = 0; if a + y >1 is discontinuous.

Q: Determine if = f(x)=Vxis uniformly continous on the interval I [0, +)

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: The function z is defined by z(x, y) = x y-3 y Find A z and dz when x= 3, y= 5, Ax = - 0.04 and A y…

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Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: The function f has continuous second derivatives, and a critical point at (-8, -7). Suppose frz(-8,…

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Q: Show that the function y = x1/2, x > 0, is strictly concave

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Q: For the function f(x) =-X find f"(X), f"(0), f’"(1), and f"(- 1). "(X) = O I7

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Q: 10. Let F(x, y) = 1 + v4 – y². (a) Evaluate F(3, 1). (b) Find and sketch the domain of F. (c) Find…

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Q: 8. Show that the function f(2)= 2 is continuous everywhere but not differentiable anywhere.

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Q: find the critics (local max, lo cal min) Of the function f(xcy)= -x5+ Dy3+27x-24y+3

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Q: express the extreme value theorem for functions of two variables . find the absolute maximum and…

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Q: 2. Sketch the domain of the following functions: a) f(x, y) = b) f(x, y, z)= 2-x-y - eª %2 In(4-x² -…

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Q: 3. Verify that the function f(x) defined over the interval [0, 3], satisfies Rolle's theorem. Find…

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Q: Check that the equation x³ + y³ + 2³ = x + y + z implicitly defines at least one differentiable…

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Q: Find the function r that satifies the following condition. r'(t)=(3t2,4t3,2t); r(1)=(-2,-5,-9)…

A: Given,          r't= 3t2 , 4t3 , 2t  , r1=-2,-5,-9

Q: Let f(x, y) = √√/175 – 3x² – 4y² Evaluate f(1,4)

A: Given :To Find :

Q: Check that the equation x³ + y³ + z³ = x + y + z implicitly defines at least one differentiable…

A: Solution

Q: If f is a function defined from R to R, is given by f(x) = 5x - 3 then f -(x) is given by %3D -- 20…

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Q: . Show that each function is not analytic at any point but is differentiable along the indicated…

A: “Since you have posted multiple questions with multiple sub parts,we will provide the solution only…

Q: 15. For f (x) = x ^ 3 -12x + 10 the interval where f (x) is concave downward is: A. (0, ) b. (-00,…

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Q: The function(x)= is concave down on which interval?

A: Given: f(x)=1x2+1

Q: Can the level surface x^2 + y^2 + z^2 − 5 = 0 be expressed as the graph of a function f(x, y)?

A: Level surface isif possible then we have to express as it the graph of a function f(x, y).

Q: Let f(2)=u+iv be an analytic function. Given that u=v² show that f(z) is a constant.

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: I. Determine whether or not the function x2 + 2y if (x, y) # (0,0) f(x, y) 1 er-y if (x, y) = (0,0)…

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