Divide and check your answer. x4 - 4x3 4x - x +4 X-4 x4 - 4x – X+4 X-4 = (Simplify your answer.)
4. Divide x4 - 5x + 5x2 + 4x - 4 by x - 2 and express the result in quotient form. (T/C-3 Marks)
Differentiate f(x) = 24 – 4.x +3 3+1 (1) f'(x) = [(x4–4x+3)/(277)]-(Vx+1)(42.3 – 4) (V<+1) z(1+1) [E{7)/(E+11–22)=(1-21)(1+34) = (x),f (1) z(I+) EN/1)-(t-rat) = (x), (£) (1-x)g = (2x),f ()
4x (x4 12 for x 1 Use the power series for (1 + x*)-1 and differentiation to find the power expansion for f(x) = n 1
Detailed answer
Find the solution to the IVP x4 y(4) – 4x®y"' +12x²y" – 24xy' +24y=0
. If not, explain why not. . x4 + 6x3 + 7.x2 – 6.– 8 27-4 3.x2 + 14.2 + 8 (e) lim- (f) lin e42 - 1 (f) lim sin(2.c) (g) lim sin?(36) x sin c (h) lim tan(5x) csc(4x) 0- 0
Determine whether the equation is exact. If it is, then solve it. (4x®y+8) dx + (x4 - 5) dy = 0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. = C, where is an arbitrary constant. O A. The equation is exact and an implicit solution in the form F(x,y) = C is (Type an expression using x and y as the variables.) OB. The equation is not exact.
Prove that x4 + 3x + 4x² + 8x + 11 is irreducible in Q[x] . Make sure to completely justify all your claims.
Find f ∘ g, g ∘ f, and g ∘ g. f(x) = 4x, g(x) = x4 (a) f ∘ g (b) g ∘ f (c) g ∘ g
Solve the exact differential equation (4x*y+sinx)dx+(x4-y)dy=0.