Show that the following subsets of C[0, 1] are isometric: {f € C[0, 1] : f(1/2) > 0} {j€ C[0, 1] : f(1/2) < 0}. and Y : - Show that C[0, 1] and C[0, 2] are isometric.

Q: Consider ∂/∂t f(tx, ty). Prove that if f is homogenous of degree n, then the attatched equation is…

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A: Let P∈L(Cn) be defined by   P(z1 , . . . , zn) = (zn , z1, . . . , zn-1)Determine whether P is…

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Q: conservative.

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Q: Let A = T(u) = T(v) = 30 03 4 and define T: R²R² by T(x) = Ax. Find the images under T of u = -7 a…

A: To solve the following

Q: Show that the following subsets of C[0, 1] are isometric: X {fe C[0, 1]: f(1/2) >0} {fe C[0, 1]:…

A: Given :              X=f∈C0 , 1 : f12&gt;0Y=f∈C0 , 1 : f12&lt;0 Show that :  C0 , 1 and C0 , 2 are…

Q: Find B and t for the space curve r(t) = N 11 ਕਰਜ |·+|· 1 +1 + 2 3 ()+( 3 +1 j, t> 0.

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Q: Suppose F(x, y, z) = (ex, 2³, y² + 2) (a.) calculate V x F (b.) let C be the line segment from (0,…

A: (a.) To find: .(b.) To find: , where C is the line segment from (0, 0, 0) to (1, 2, 3).

Q: Consider F and C below. F(x, y, z) = yzexZi + e²j + xye*²k, C: r(t) = (2 + 4)i + (t² – 1)j + (t² -…

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Q: Exercise 1: Show that the functions are orthogonal the indicated interval. a) f(x) = x, g(x)=x², x =…

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Q: Let f(x, y) = x2 − 2y and g(x, y) = xey . Show that at any point (x0, y0), the level curve of f…

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Q: Show that [0, o0) and [1, o0) are isometric.

A: We need to show that ,  [0 , ∞)  and  [1 , ∞) are isometric. We know that two metric spaces X and Y…

Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z)= In (2³-4x³ - 3y³ - 2) 1…

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