Show that the opelator Tilol defined by Y=19;)=Tx.-E] *=(h:)is Linear and bounded

Q: SUppose F(x) = dt. Find the formda 13 F (x ³) expressed using an integral. ? F (x* )= ]

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Q: Consider a linear map T : R″ → R" with the property that null(T) = range(T). (a) For n = = 2,…

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Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

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Q: Is there a twice differentiable function f R2R whose best adratic approximation at the point (1,0)…

A: Given problem is from differential calculus in several variables. We have shown that there exists a…

Q: (0, 1) = U(4 ",1– 4 ") n=D1 (Hint: taking limit is not acceptable)

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Q: Suppose f, g:C → C are differentiable. Prove that fg is differentiable and that (fg)' = f'g + fg'.

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Q: et f(x,y)= x^2-xy+y^2-y   what are the min and max values of Du f(1,-1)?

A: Given :  f(x,y) = x2-xy+y²-y  To find :  Maximum and minimum values of directional derivative at…

Q: Find the value of f(-1) when ƒ"(t) = 6(2t − 1) and ƒ'(1) = 6, ƒ(1) = 1.

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Q: 7. F- dr from (0,0) to (3,9) along the curve y=x' if F(x, y, z) = 4 xyi + 3xy'j Evaluate

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Q: Assume that f: R→ R and g: R → R are infinitely differentiable functions. Prove the following…

A: We have given that ,  are both infinitely differentiable.We need to prove that , We will use…

Q: Let i, j, k e Za and w, x, y e Zb with i, j, k all different from each other and w, x, y all…

A: Let the number of elements in the domain be equal to m, and the number of elements in Zb be equal to…