Please show your answers to at least 4 decimal places. Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the direction < - 1,1 > and (3, 2) is at the point (x, y) =

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A: Please see the below picture for detailed solution.

Q: 1) Find the linearization L(x) of f(x) at x = a. f(x) = 2x2 + 4x - 1, a =

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A: Please see the below picture for detailed solution.

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A: I am attaching image so that you understand each and every step.

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A: Topic = Volume

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Q: 4. Solve the given integral |(2* − xe*")xdx 2 a. 2x² C. In 2 3ex³ + C 4x² +3ex³ In 2 + C 2x² 2 ln 2…

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Q: would you mind typing it out I cant really read it thank you

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A: We can find the solution of the given differential equation by using the variable separable method.

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A: I am attaching image so that you understand each and every step.

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A: Given linear operator A=2456     and  basis   S= 1-2  ,3-7

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A: By using function theory

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A: See the details solution in below

Q: find volume of shell y=x y=x^2 over x axis

A: This is equivalent to rotating R2 about the line y=0. Since neither of the curves are touching the…