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6. Justify briefly (max two lines) if the following statements are true or false. Answers with...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20...
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
y 4 3 2 O 1 -4 -2 - 1 1 2 3 4. D 6...
y 4 3 2 O 1 -4 -2 - 1 1 2 3 4. D 6 7 8 9 -1 . lim f() lim f (x) (t) lim f (x) (a) +-3 (g) +0 lim f (x) (b) +-3+ (h) 1+0+ lim f (1) limf (1) (c) 17-3 (i) 2-0 lim f (x) (d) () 1-2- limf () lim f (x) (e) 16-27 (k) 1+2+ lim f (x) (1) 2+2 lim f(x) (m) +4- lim f (0) lim f(x) (s)...
14.7. Taylor's theorem and Max/Min values. A statement of Taylor's theorem for functions of two variables...
14.7. Taylor's theorem and Max/Min values. A statement of Taylor's theorem for functions of two variables and an example are in Part I (section 7) of my online notes if you didn't get it in class. H. Compute the Hessian of the function f(x,y) = y?e evaluated at the point (0,2), ans (lo 8 I. Use the formula involving the gradient and Hessian for z = Q(x, y) to determine the second order Tavlor polynomial for the functions. You should...
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a....
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a. By using the two path test we can deduce that the limit does not exist b. By using the two path test we can deduce that the limit exists c. The limit is 2 d. None of the above O a. O b. O c. O d. 2) Let f(x,y) Vx+1-y+1 xy Then lim f(x,y) (xy)+(0,0) a. is 0 b.is c. is 1 d....
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z =...
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
Answer All Questions. (9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the...
Answer All Questions.
(9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the domain of f. (10) A thin metal plate, located in the xy-plane, has temperature T(x,y) at the point (x,y). The level curves of T are called isothermals because at all points on such a curve the temperature is the same. Sketch some isothermals if the temperature function is given by 100 T(x, y) = 1 + x2 + 2y2 (11) Show that lim (z2...
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z =...
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z = 2x2 + 2xy + y2 + 1 at the point P(-1, -3, 18). 2) Find all critical value(s) and classify as maxima/minima/saddle points/none. F(x,y) = 2x + 4y - x2 - y2 - 3 3) Find the directional derivative of z = xy +x in the direction of v= <3,-4> at the point Q(1,4). Also find the direction of maximum increase at this point....
Real analysis 10 11 12 13 please (r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and li...
Real analysis
10 11 12 13 please
(r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
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....
1. Find the first and second partial derivatives: A. z=f(x,y) = x2y3 - 4x2 + x2y-20 B. z=f(x,y) = x+ y - 4x2 + x2y-20 2. Find w w w x2 - 4x-z-5xw + 6xyz2 + wx - wz+4 = 0 Given the surface F(x,y) = 3x2 - y2 + z2 = 0 3. Find an equation of the plane tangent to the surface at the point (-1,2,1) a. Find the gradient VF(x,y) b. Find an equation of the plane...
y 4 3 2 O 1 -4 -2 - 1 1 2 3 4. D 6 7 8 9 -1 . lim f() lim f (x) (t) lim f (x) (a) +-3 (g) +0 lim f (x) (b) +-3+ (h) 1+0+ lim f (1) limf (1) (c) 17-3 (i) 2-0 lim f (x) (d) () 1-2- limf () lim f (x) (e) 16-27 (k) 1+2+ lim f (x) (1) 2+2 lim f(x) (m) +4- lim f (0) lim f(x) (s)...
14.7. Taylor's theorem and Max/Min values. A statement of Taylor's theorem for functions of two variables and an example are in Part I (section 7) of my online notes if you didn't get it in class. H. Compute the Hessian of the function f(x,y) = y?e evaluated at the point (0,2), ans (lo 8 I. Use the formula involving the gradient and Hessian for z = Q(x, y) to determine the second order Tavlor polynomial for the functions. You should...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
2x+5xy* 1) Let f(x,y) = *3+x3y2 Which among the following is true about limf(x,y)? (x,y)--(0,0) a. By using the two path test we can deduce that the limit does not exist b. By using the two path test we can deduce that the limit exists c. The limit is 2 d. None of the above O a. O b. O c. O d. 2) Let f(x,y) Vx+1-y+1 xy Then lim f(x,y) (xy)+(0,0) a. is 0 b.is c. is 1 d....
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
Answer All Questions.
(9) Let f(x,y) = 1+ 4- y2. Evaluate f(3,1), find and sketch the domain of f. (10) A thin metal plate, located in the xy-plane, has temperature T(x,y) at the point (x,y). The level curves of T are called isothermals because at all points on such a curve the temperature is the same. Sketch some isothermals if the temperature function is given by 100 T(x, y) = 1 + x2 + 2y2 (11) Show that lim (z2...
UU. LIUC JUULIULIS. 1) Find the equation of the tangent plane to the graph z = 2x2 + 2xy + y2 + 1 at the point P(-1, -3, 18). 2) Find all critical value(s) and classify as maxima/minima/saddle points/none. F(x,y) = 2x + 4y - x2 - y2 - 3 3) Find the directional derivative of z = xy +x in the direction of v= <3,-4> at the point Q(1,4). Also find the direction of maximum increase at this point....
Real analysis
10 11 12 13 please
(r 2 4.1 Limit of Function 129 se f: E → R, p is a limit point of E, and limf(x)-L. Prove that lim)ILI. h If, in addition, )o for all x E E, prove that lim b. Prove that lim (f(x))"-L" for each n E N. ethe limit theorems, examples, and previous exercises to find each of the following limits. State which theo- rems, examples, or exercises are used in each case....
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....
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