Kindly solve in 20 minutes and get the thumbs up please show me neat and clean work for it by hand solution neededKindly solve ASAP in the order to get positive feedback with hundred percent efficiency (a) Given is the function h(x, y) = (y − 1)(x + 1).(i) Draw the level curves for h(x, y) = c for c= -1,0, 1 in thexy-plane. Label curves clearly with the appropriate value of c.Show all your working.(c)(ii) In the drawing of the previous part, clearly mark pointsP₁ = (-1,3),P₂ = (-₁1) and P3 = (-1,-1). Draw a direction inwhich h neither increases nor decreases at P₁. Draw thegradient vector of h at P₂. Draw the direction of the steepestdecrease at P3. Show your working and justify your choices.(b) Consider the following second-order differential equationdy+dy(1) Find the general solution of the equation.(ii) Use the general solution from part (i) to evaluate lim y(x).#448Calculate the particular solution ofd'y(iii) Find the particular solution satisfying y(0) =y (0) = √3.d(0)(0) = 0 and+y=0.(0)== 0.d³y= 0 and==sin(x) with y(0) = 0,

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(a) Given is the function h(x, y) = (y - 1)(x + 1). (1) Draw the level curves for h(x, y) = c forc = -1, 0, 1 in the xy-plane. Label curves clearly with the appropriate value of c. Show all your working. (ii) In the drawing of the previous part, clearly mark points P₁ = (-1,3), P₂ = (-1, 1) and P₁ = (-1,-1). Draw a direction in P3 which h neither increases nor decreases at P₁. Draw the gradient vector of h at P₂. Draw the direction of the steepest decrease at P3. Show your working and justify your choices. ) Consider the following second-order differential equation d2y dx² dy + +y = 0. dx (1) Find the general solution of the equation. (ii) Use the general solution from part (i) to evaluate lim y(x). #448 (iii) Find the particular solution satisfying y(0) = 0 and y (0)=√3. dy (0) = 0 and Calculate the particular solution of dy (0) -(0) = 0. d³y da³ =sin(x) with y(0) = 0, =

(a) Given is the function h(x, y) = (y - 1)(x + 1). (1) Draw the level curves for h(x, y) = c forc = -1, 0, 1 in the xy-plane. Label curves clearly with the appropriate value of c. Show all your working. (ii) In the drawing of the previous part, clearly mark points P₁ = (-1,3), P₂ = (-1, 1) and P₁ = (-1,-1). Draw a direction in P3 which h neither increases nor decreases at P₁. Draw the gradient vector of h at P₂. Draw the direction of the steepest decrease at P3. Show your working and justify your choices. ) Consider the following second-order differential equation d2y dx² dy + +y = 0. dx (1) Find the general solution of the equation. (ii) Use the general solution from part (i) to evaluate lim y(x). #448 (iii) Find the particular solution satisfying y(0) = 0 and y (0)=√3. dy (0) = 0 and Calculate the particular solution of dy (0) -(0) = 0. d³y da³ =sin(x) with y(0) = 0, =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter14: Discrete Dynamical Systems

Section14.3: Determining Stability

Problem 1YT

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