Tính gradient của hàm số f(x, y) = x^2-2x-4y^2-4y.

We know that $x^2 - y^2 = (x + y)(x - y)$. Substituting, we see that $x ... Factoring, we find that $x^2 - 2x - 3 = (x - 3)(x + 1) = 0.$ Therefore, $p ... y. (2x+5y+3) = 5 and x. (5x 4y+2) = 5, so sin e these are equal, the ODE is exa t. The integral will have the form F(x; y) = R. 2x + 5y + 3dx = x2 + 5xy + 3x + ... Apr 17, 2025 ... ... ( x ) and ( y ). Steps to Rewrite the Equation. Rearrange the equation: [ x^2 - 2x - 4y^2 - 8y = 7 ]. Complete the square for ( x ): Take the ... Mar 5, 2021 ... ... y) = x2 + y2 - 2x - 4y is i + j. Find all points at which the direction of the fastest change of the function f (x, y) = x2 + y2 - 2x - 4y is i ... ... (-2) (x + 1) + 4/y-2). 2x-4y+z d) f(a)=√4-+2+2 = X. =-5. 2. S. X. DF (3) (x - 2 ) = ( ½, ÷ ) ( ~. १. The tangent plane is f. √ = x + √ √ 2 4 + 2 = 2√2. DF (a) = (. Mar 13, 2017 ... F : R2 → R2, F(x, y) = (0,x). (a) Find all eigenvalues and ... 2x - 4y + 6z. 3x - 6y + 9z.. . (a) Find a basis b = 1u,v, ~wl for ... To substitute, you have two choices to isolate variables, in both equations, solving for x is the easiest. In the first equation, you could divide by 2 to get x ... Using the following equation, x 2 + 2x + y 2 + 4y = 20 we get the centre as (-1, -2) and radius r as 5. ... two ones you will get x3, x2, or x. d) Using the same reasoning you ... 6) 8(x2 -2)(2x4 + 2x2 + 4). 7) (3x3 + 8)(3x3 – 8). 8) 2(5x2 – 32). Pg 77: 1) (x ... Minimize x2 + y2 + z2, with 2x + y − z − 6=0 ⊕. 2x = 2λ. . . Lagrange ... (x 2 + y 2 + 1)dxdy = (r 2 + 1)rdrdθ = 2π. +. = 2π. = 4. 2. ·. 4. 2. 0. 0. 0. 3. Page ...