Show that the operator U is positive U: 1² ([0,1]) → L²([0,1]), Uƒ (x) = X[{0,1] [~*\f(t)\dt

Q: If r'(t) = (1,21,3r*) and r(0) = (0,1,2) then r(t) equals %3D (a) (1,r°,r'). (b) (1,r",r')+ (0,1,2)…

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Q: Suppose f(): R" → R (n EN). (a) What is directional derivative of f(-) at x ER" in direction v ER"?…

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Q: Let f(x, y) = x* /I Evaluate f(3, 0)

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

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Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

A: Letandfind the derivative

Q: Let f(x, y) = e²x* %3D Evaluate f(3, 5)

A: Given :   f ( x, y) = exy x4   point ( 3,5)

Q: Pron a. If u = f(x, y), where r = e' cost, and y = e' sint, show that (3)³ + (3) ² - - ² [(-)* +…

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Q: f(x,y) af ?x af ду = af ду X 2x² + 8y² f(x, y) = tan af ?x (5)

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity