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- The cubic function y = ax3 + bx² + cx + d pass through (0, -6), (1, -2) and tangent to the line 3x – y = 6 at (2, 0). What is the equation of the cubic which satisfies the given conditions? Select the correct response: O y = 6x3 – x² + 4x – 7 у %3D 4х3 — 7х2 + х — 6 - y = 4x³ + 7x2 – 6x + 1 y = x3 – 4x2 + 7x – 6 |ts) Find two linearly independent solutions of 2x²y" - xy + (2x + 1)y=0, x > 0 of the form Y₁ = x¹(1+ a₁ + a₂c² + a3x³ + ...) Y₂ = x²(1 + b₁c + b₂x² + b3x³ + ...) where T1 T2. Enter T1 T2 a1 = a₂ = a3 = b₁ b₂ TE b3 N - || || || || =Find the extrema of (x+1)(y+1)(ax+by+c) Where a=8,b=7,c=6.
- 5c) Find the partial derivatives? y = 2x2+3xz+85w-8z2The equations æy? + 2xzcos(u) + ye" = 4 and x³yz + xe" – 8u²v² = 24 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) = (풍,0). Find (),y at P. | du dz 12,y Türkçe: xy? + 2xzcos(u) + ye" = 4 ve x³yz + xe" – 8u?v² = 24 denklemleri P noktası (x,y,z)=(1,1,1) ve (u, v) = (4,0) civarında x,y ve z'nin fonksiyonu olmak üzere u ve v için çözümlü olsun. P'de (u)zy'yi hesaplayınız.) dz O 64,00 O 4,00 O -10,00 O -0,50 O -80,00 "GenFind V. (V x F), if F(x, y, z) = 7e#²i+9xe®j – ev²k. V·(V × F)
- Without solving, classify the following equations as to: separable, homogeneous (the degree), exact, linear, Bernoulli, or Ricatti (d) y + 5y? + 2ry = 3r*. %3D dy (e) y dr +r dy - 0. (f) = () y dr = (y- ry²) dy(h) r dy ye/y. - r.The equations ry? + 5xzcos(u) + ye" = 10 and x³yz + xe" – 10u2v² = 30 are solved for u and v as functions of x, y and z near the point P where (x,y,z)=(1,1,1) and (u, v) %3D (풍,0). Find (을),y at P. du Türkçe: zy? + 5æzcos(u) + ye" = 10 ve r³yz + xe" – 10u²v² = 30 denklemleri P noktası (x.y,z)=(1,1,1) ve (u, v) = (5,0) civarında xy ve z'nin fonksiyonu olmak üzere u ve v için çözümlü olsun. P'de ()2y yi hesaplayınız.) du dz -25,00 O 80,00 10,00 O - 100,00 -0,20Find ∂y/∂x1 and ∂y/x2 y = 2x13 − 11x12x2 + 3x22 y = 7x1 + 6x1x22 - px23 y = (2x1 + 3)(x2 - 2) y = (5x1 + 3)(x2 - 2) y = (2x1 - 3x2) / (x1 + x2) y = (x12 - 1) / (x1x2)