The second order Taylor method is (derivative is taken with respect to t.) h Yi+1 = Y; + h| f (ti, Yi) +7ƒ'(ti, Yi) + n( f(² ) Apply this method to the model problem y' = λy, (Reλ < 0) to find and plot the region of stability for this method. Also found the restriction on h for stability if λ is real.

Q: Show that the directiona f(x, y, z) = z²x + y ² at ( X (1/15" + ) ; 255. them

A: fx,y,z=z2x+y3 P1,1,2v→=15i+25j We know directional derivative Dv→fP=∇fP.v→v→

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A: our objective is to find the required derivative

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A: Given: u=lx+my v=mx-ly   To show: ux=-vy and uy=vx

Q: 7) A building is 300 feet tall. It casts a 165 foot long shadow. A statue near the building is 40…

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Q: 2. Find the gradient of the function f(x, y) = ln(x² + y²) at the point(1, 1).

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: The given function is

Q: Q3: Find gradient of the following function at given point 2) g(x, y) = y – x². (-1,0)

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Q: Parameterize x(y) = √√y+5y using y = t Ans=

A: The parameterization of x(y)  using  y = t  is  x(t)=t​+5tExplanation:Given expression is…

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A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…