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(-) Determine the approdato change of the area de a triangle. Aber where is the length...
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine...
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
Suppose f(x,y)=xy(1−10x−4y)f(x,y)=xy(1−10x−4y). f(x,y)f(x,y) has 4 critical points. List them in ...
Suppose f(x,y)=xy(1−10x−4y)f(x,y)=xy(1−10x−4y). f(x,y)f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, determine whether the critical point a local maximum, a local minimim, or a saddle point. First point (____________,__________) Classification: Second point(__________,__________) Classification: Third point (___________,_________) Classification: Fourth point (__________,_________) Classification:
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent p...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
(8) Find the area of under the graph of y=x?, y = x between x =...
(8) Find the area of under the graph of y=x?, y = x between x = 0 and x =1. (9) Evaluate, (a) using trapezoidal rule, (b) using Simpson's rule: dx n=4 (10) Solve the initial value problem. f "(x) = x2 + x +1; f'(0)=2, f(0) = 3. (11) Solve : (x2+1) + 2xy = x' + x (12) Solve : i - celoy, y(t) =-2 (13) Find partial derivatives up to second order: f(x, y)=(x+xy+y)(x +xy+1) f(x, y)...
ECON 1111A/B Mathematical Methods in Economics II 2nd term, 2018-2019 Assignment 6 Show your step...
ECON 1111A/B Mathematical Methods in Economics II 2nd term, 2018-2019 Assignment 6 Show your steps clearly Define the definiteness of the following A-[1 5 a. b. 1 4 6 d. D= -2 3 1 -2 1 2 E 2 -3 1 2. Is the function f(x,y) - 7x2 + 4xy + y2 positive definite, negative definite, positive semidefinite or negative semidefinite? Find the extreme values for the following functions and identify whether they are local maximum, local minimum, and saddle...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x,...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the ...
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...
14. (a) Determine all possible critical point(s) of f(, y) = x2 + xy + y2...
14. (a) Determine all possible critical point(s) of f(, y) = x2 + xy + y2 - 3.c - 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT). 15. Find a point on the hyperboloid 2z = x2 - y², where the tangent plane is parallel to the plane x - 3y - 2 = 1.
14. (a) Determine all possible critical point(s) of f(x, y) = x2 + xy + y2...
14. (a) Determine all possible critical point(s) of f(x, y) = x2 + xy + y2 – 3x – 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT).
Compute the partial derivatives of the function at the given point, and determine what the total...
Compute the partial derivatives of the function at the given point, and determine what the total derivative would be if the function was differentiable there; then determine whether it is differentiable or not by definition; that is, determine whether or not 0. 22+y2 (x,y) # (0,0) fão + n) – $(20) - Df#, (h) lim ho hi 4. h(x, y) = 0 (2,y) = (0,0) at (0,0); 5. g(x, y, z) = x + 3y - 2 - 1 at...
In Problems 1-3, solve the given DE or IVP (Initial-Value Problem). [First, you need to determine what type of DE it is.) 1. (2xy + cos y) dx + (x2 – 2 siny – 2y) dy = 0. 2. + cos2 - 2ary dy dar y(y +sin x), y(0) = 1. 1+ y2 3. [2ry cos (x²y) - sin r) dx + r?cos (r?y) dy = 0. 4. Determine the values of the constants r and s such that (x,y)...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
(8) Find the area of under the graph of y=x?, y = x between x = 0 and x =1. (9) Evaluate, (a) using trapezoidal rule, (b) using Simpson's rule: dx n=4 (10) Solve the initial value problem. f "(x) = x2 + x +1; f'(0)=2, f(0) = 3. (11) Solve : (x2+1) + 2xy = x' + x (12) Solve : i - celoy, y(t) =-2 (13) Find partial derivatives up to second order: f(x, y)=(x+xy+y)(x +xy+1) f(x, y)...
ECON 1111A/B Mathematical Methods in Economics II 2nd term, 2018-2019 Assignment 6 Show your steps clearly Define the definiteness of the following A-[1 5 a. b. 1 4 6 d. D= -2 3 1 -2 1 2 E 2 -3 1 2. Is the function f(x,y) - 7x2 + 4xy + y2 positive definite, negative definite, positive semidefinite or negative semidefinite? Find the extreme values for the following functions and identify whether they are local maximum, local minimum, and saddle...
DUE DATE: 23 MARCH 2020 1 1. Let f(x,y) = (x, y) + (0,0) 0. (x, y) = (0,0) evaluate lim(x,y)=(4,3) [5] 2r + 8y 2. Show that lim does not exist. [10] (*.w)-(2,-1) 2.ry + 2 3. Find the first and second partial derivatives of f(x,y) = tan-'(x + 2y). [16] 4. If z is implicitly defined as a function of x and y by I?+y2 + 2 = 1, show az Əz that +y=z [14] ar ду 5....
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...
14. (a) Determine all possible critical point(s) of f(, y) = x2 + xy + y2 - 3.c - 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT). 15. Find a point on the hyperboloid 2z = x2 - y², where the tangent plane is parallel to the plane x - 3y - 2 = 1.
14. (a) Determine all possible critical point(s) of f(x, y) = x2 + xy + y2 – 3x – 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT).
Compute the partial derivatives of the function at the given point, and determine what the total derivative would be if the function was differentiable there; then determine whether it is differentiable or not by definition; that is, determine whether or not 0. 22+y2 (x,y) # (0,0) fão + n) – $(20) - Df#, (h) lim ho hi 4. h(x, y) = 0 (2,y) = (0,0) at (0,0); 5. g(x, y, z) = x + 3y - 2 - 1 at...
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