Which of the following transformations are linear? 4 0 A. T(f(t)) = f(t)dt from P₂ to R B. T(f(t)) = f'(t) +8f(t) from C∞ to Co □c. T(f(t)) = f'(t) + 4f(t) + 2 from C∞ to Co D. T(f(t)) = f(3) from Pg to R OE. T(f(t)) = 8( f(t))² +6f(t) from Co to Co

Q: Which of the following transformations are linear? (a) T₁: R² R², T₁ R², T₂ I Y = Y = xy I (b) T₂:…

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Q: f(x, y) = 4x² + 5y² and æ = t, y = t? Use the chain rule to find df take the following steps. dt (a)…

A: Given f(x, y) = 4x2+5y2 and x=t, y=t2 We have to find dfdt using the chain rule.

Q: . Let r(t) = (t², 1 t, 4t). Calculate the derivative of r(t) · a(t) at t = 6, assuming that a(6) =…

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Q: Let f(x, y, z) = x³e" Vz² + 5 and let x = rt², y = r2t², and z = sin(t) cos(r). (a) Draw a tree…

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Q: Which of the following transformations are linear? Select all of th ore than one correct answer. Be…

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Q: Find the partial derivatives of the function f(x, y) = | cos(4t – 5t – 7) dt

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Q: (a) Find all second partial derivatives of f(x, y) = e² + tan(x + y?) (b) Find and classify the…

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Q: F (x) = f (t³ – t)°dt. Find the derivative of O 5(t – t)* (3t² –- 1) (23 – z)* O 5(2³ – z)“ O 3t2 –…

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Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

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Q: dy dx (²), y(a)= A. (a) Show that by introducing the new dependent variable v(x) by the relation y =…

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Q: (c) Use the chain rule to find the derivative of the function z = 2xr*y³ – ry² along the curve given…

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Q: (b) Note that by the chain rule and implicit differentiation, dI aSI – bI aSI + -aSI 6 1 – 1+ dI bI…

A: Given thatI is a function of tand S is a function of tBy chain rule and implicit differentiation…

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Q: dw dw as a function of t, both by using the chain rule and by expressing w in terms of t and…

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Q: If r(t) is differentiable, r(0) 2 * \r' (t)\ dt > 7 True False r(0) = = (1, 0, (1, 0, 1), and 1),…

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