. Let f (x) = cx 3 and S X = [0, 2] (X is continuous and c is a constant). a. What value of c will make f (x) a valid density? b. What is P (X = 1)? c. What is P (X

Q: Indicate whether the following statement is true or false. Let f (x, y) be any real valued function…

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Q: Let f(x,y) = and let g(x, y) 4xy¹ 4x4 + 4y4 0 if(x, y) = (0,0) 0 if (x, y) = (0,0) 5xy 10 5x² + 5y20…

A: f(x,y)=4xy44x4+4y4if (x,y)≠(0,0)0if (x,y)=(0,0)g(x,y)=5xy105x2+5y20if (x,y)≠(0,0)0if (x,y)=(0,0)

Q: 3. Consider a function f(x) = sin() : R → R. x²+1 (a) Show that f is continuous on R.

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Q: Evaluate f(x, y, z) dV for the specified function f and box B. f(x, y, z) = z3; 13 x < 8, 1 S ys 5,…

A: Given

Q: If f is continuous function on a, b|, then Sæf(x)dæ = x J° f(x)da S. f(x)dx :Select one a. False b.…

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Q: At what points of R is the following function continuous? xy if (x-y) (0.0) f(x y) = 7x +y 0. if…

A: We have to find set of continuity of given functions.

Q: 1. Let f(u, v) be a continuously differentiable function. Let u = e*, v = e³. Show that u²fuu + v²…

A: Given that f(u,v) is a continuously differentiable function, and u=ex, v=ey then show that…

Q: 15. Let f(x, y) = 22 if (x, y) ‡ (0,0), and f(0,0) = 0. Is ƒ continuous at (0,0)? x+y

A: