3. Let f, g to be two continuous functions on [a, b] and f(a) ≥ g(a), f(b) ≤ g(b). Prove that Exo € [a, b], s.t. f(xo) = g(xo).

Q: 18. Let f(x) be continuous on [1, 3] and f (1) = 4, f(3) = 20. Show using the intermediate value…

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Q: 4. Prove that f(x, y, z) = 2 - 1 x² + y² is continuous in all its domain.

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Q: Let F be a continuous function on [a, c} , where a < b< e, and F(z) dz = 6, F(2) dz = 9 A. Evaluate…

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Q: 1. Let h : R → R be some twice-differentiable function. Define f(x,y) =h() for all x ≠ 0. Show that…

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Q: → R be a function defined by 3x² + x+5 f(x) = not continuous at x = = 0.

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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: Let h : R → R be some twice-differentiable function. Define f(x,y) = h(x) for all x ≠ 0. Show that…

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Q: 2: If f(x) and g(x) are continuous on (a,b]and if f =[s . Prove that 3cela,b] such that f(c)=g(c).…

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Q: sider the function f (t) = –2t³ – 6t² + 8 on the interval [-1, 2]. of values of c for which such…

A: f'(c) = f(b) -f(a) /b-a

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: Let f, g to be two continuous functions on [a, b] and f(a) ≥ g(a), f(b) ≤ - Prove that co € [a, b],…

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