1. Consider the function z = x In(1+ y²), if x 2-t and y= Vf, use an appropriate form %3D dz at t =1. dt of the chain rule to find

Q: əz Use chain rule to find z = x² + 3wxy + w², with x = 2t + 1, y = et and w = 3 – t2.

A: The aim is to find, The formula for chain rule is,

Q: Show that the function u(z, t) : satisfies ua = %3D %3D a2t2-2

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Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

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Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

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Q: Find the linearization L(x) of f (x) = tan x at a =

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Q: Əs' at (1) z = x²+ y², x= s+2t, y = 3st (2) z = sinxcosy, x s-t, y = s² +t³ %3D (3) z = e" tany, x =…

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Q: z = sin x cos y, = VE, y = 1/t x =

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Q: Find y as a function of a if 2'y" + 6zy/ - 36y = 0, %3D y(1) = 1, y(1) = 5. %3D y =

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Q: Determine the magnitude and direction of the largest change 2 2 (x² + y²)z at the point M (1, -2,1).…

A: Introduction How sharply a curve rises determines its magnitude. It is simplest just examine the…

Q: L(x) = b) Use the linearization to approximate 125.1 ~

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Q: Discuss the sinqulas itres and poles of F(Z) = zesin2 (z-2)(2-1X2²16Z+6)(z+7)(z'4) %3D

A: A point z0 is the singularity of the function f(z) if f is not analytic at z0 but every neighborhood…

Q: Use the Fundamental Theorem of Calculus Part I to find dh/dx given h(x) = cost dt (Hìnt: need…

A: Answer:  By fundamental theorem of calculus  Let fx=∫axbx gt. dt   dfdx=gbx.b'x-gax.a'x

Q: First write the function y = Vx2 +1 as a composition of y = f(u) and u = g(x), and then dy apply…

A: y=x2+1y=f(u), u=g(x)To find:dydx

Q: Determine which of the following pairs of functions are linearly independent. NO_ANSWER 1. f(0) =…

A: The linear dependency of functions can be evaluated using the value of the Wronskian of those…

Q: 3. Find all functions from X = {a,b} to Y = {p,r, t}.

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Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

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Q: Find the image of the line z =3 +iy under f(z) = e

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Q: yz, x = 02, y = r+ 70, = M Z =r- 70 (a) Find ôw/ðr and aw/80 by using the appropriate Chain Rule. dw…

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