plve the piecewise linear ODE, y' – y= f(x), y(0) = 1, where f(r) = 1 when 0 < x<1 and f(r) = -1 when x > 1. What is y(2)? Ro

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Q: 3. find the derivative of the function at Po in the direction of u. f (x, y,z) = 3e* cos yz,…

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Q: Integrate the function f (z) = (z – 8i)- from z = 0 to z = 4 + 4i along the line x = y.

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

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Q: 3r²y Determine if ƒ is continuous at (0,0) where f(r, y) = { r4 + 2y2 (x, y) + (0,0) (1, y) = (0,0)

A: for f(x) to be continuous at (0,0) limx→0+,y→0+f(x,y)=limx→0-,y→0-f(x,y)= f(0,0)

Q: Approximate X f(x) = e*over the interval [- 4, – 2] using 2 subintervals.

A: In this problem, Simpson 1/3rd rule is used to find the approximate value of e^x over the interval…

Q: dz Use an appropriate form of the chain rule to find dt z = 8x"y³; x = t°, y = t Enter the answer in…

A: Topic :- Differentiation

Q: Use the Chain Rule to find dz where z = 2x cos y, x=t, and y = 5t. dt dz dt (Type an expression…

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Q: valuate S. F · ds, where F(x, y, z) = (z, x, y) and c(t) = (t, t², t³), 0 < t < 1.

A: F(x,y,z)=(z,x,y)

Q: 8. The second directional derivative of a function f(r, y) is Df(x, y) = D« [Duf(x,y)]. If f(r, y) =…

A: NOTE- as we are allowed to answer 1 question in one session so i have answered question 8 for you.…

Q: Use the differential dz to approximate the change in z = √4 − x2 − y2 as (x, y) moves from the point…

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Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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Q: ) Find the linearization of f(x) = sinx at x = 0.(b) Compute dy if y = x2 +x and x changes from x =…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find fz and fy- f(z, 9) = [" 9eª dt f.(x, y) = f,(x, y) =

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Q: Find fr and fy- f(x, y) = 7e dt f-(x, y) = f,(x, y) =

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Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: 3. Given the function f(x, y, z) = In(x² + y² – 42²), find the directional derivative f, in the…

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Q: ) Find the linearization L(x, y) of the function f(x, y) = ez+y at (0,0). Use it to estimate f(0.01,…

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Q: дz in terms of r and t using chain rule if given that z=√√√4x² - y²₁ 1) Find and simplify dt x=r…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Integrate the function f (z) = (z – 8i)² from z = 0 to z = 4 + 4i along the line x = y. 2

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Q: Find the derivative of the function at Po in the direction of A f(x,y,z) = 3 e* cos (yz), Po(0,0,0),…

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Q: Find fr and fy. 2e" dt f (x, y) = 2, f.(r, y) = f„,(x, y) =

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Q: Find the differential of f(x, y) = Vr2 + y³ at the point (2, 3). df = Then use the differential to…

A: given function is f(x,y) =x2+y3 we know, for the function z = f(x,y), the total differential of the…

Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

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Q: 0Y Find the direction derivative of fcxy)=xy at the paint (2,1), by the dirction of v- i-j

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Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = x2 + 2y2 – 3z?, Po(1,…

A: We can solve this as follows:

Q: Find fz and fy- Te dt f(x, y) = 5 f.(x, y) f,(x, y) : %3D

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Q: f (x, y) = 3x^3 −9x+9xy^2. Use the second derivative test to classify the critical point (1,0) as a…

A: Recall: second derivative test : (i)  Firstly find critical points . i.e, fx(x,y) =0 and…

Q: Disccus the hatural of the Critical points: f(x,y) = 3xy-x²-y?

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Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: Find fyy for f(x, y) = e* In(y).

A: The given function is fx,y=exlny.

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = xy + yz + zx, Po(1,…

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Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

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Q: Find the differential of f(x, y) = 3+y² at the point (2, 3). df: ((3x^2)dx+(2y)dy)/(2sqrt(x^3+y^2))…

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Q: e-(z-1)2-y 1 (r, y) # (1,0) If f(r, y) = (I-1)2+y (r, y) = (1,0) %3D is continuous at (1,0), what is…

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Q: 3. Let f(x, y) = In 2x + 4y, find the directional derivative of f(x, y) in the direction of at the…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 3 ex cos (yz),…

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Q: 4. Given f(x, y) = arctan(x + 2y). Find the local linear approximation of f at (1,0) and use it to…

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Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) = sin(x), a = 2…

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Q: Integrate the function f (z) = (z - 8i)² from z = 0 to z = 4 + 4i along the line x = y.

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Q: Find the first partlal derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 9yz? %3D…

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Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: Tir Find the general function M(x, y) so that (xM(x, y) – y) dx + (sec² y – ) dy = 0 is exact y-ln…

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Q: Let f Cx, yJ=N8,?+y° Find fx Co,0)

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Q: Find the direction at which the function f(x, y, z) = x In(e' – xz) increases fastest at (-3,0, (0,…

A: Sorry I cannot recognize your given points. So I provide only methods of problem you can easily…

Q: A) Use the chain rule to find dt where wxty,x = sint + cost y cost- sint.

A: We will use chain rule to find the answer :)