2 4-x Find the area in the first quadrant bounded by the coordinate axes and the graph of y = 5 The area is (Type an exact answer, using t as needed.)

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A: Topic = Derivative

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Q: Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3 , by using the Chain Rule dt

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A: Note:- As per your request i am solving sub part d and e from given sub parts

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A: A detailed solution is given below

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A: Given vector x=etcost, y=etsint, z=etr→(t)=<etcost, etsint, et>

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Q: Flnd the maximum rate of change of f (x.y) =e*²+e*+2y at P (2,1) 29 e4 V 29 e 16 O 7e4 O Viet

A: gradient of function fx, y=ex2+ex+2y, at 2, 1

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A: let I=∫sin θ ln(cosθ) dθ Integration By parts: ∫udu=uv-∫vdu u=ln( cosθ) ; du=1 cosθ-sinθdθ=-tanθdθ…

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A: we have to find fxx and fyy.

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Q: Q1) Suppose w = +, x = cos? t, y = sin? t, z = ; dw at t = 3, by using the Chain Rule Evaluate dt

A: Topic = Derivative

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Q: Evaluate the following limits for h(x) = { 1- 5z 120 (i) lim h(r) (ii) lim h(x) (ii) lim h(z)

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A: Given problem:-