Question #5 5.) Prove that F4(x) 4x(1 - x) is not structually stable. Prove that Fe(a)-4x(1-x)is...
Given the function f(x) = 4x +5 defined on the interval (0, 3, denote by fe the even 3,3 of f extension on Find fep, the Fourier series expansion of fe плг пте ao + 2 bsin fer (x) а, COs n-1 that is, find the coefficients ao an, and bn With n> 1 ao ат W |1 l Given the function f(x) = 4x +5 defined on the interval (0, 3, denote by fe the even 3,3 of f...
Direct Proof For ∀x ∈ R, if 0<x-3 then 7< 4x. Prove by contraposition For ∀x,y ∈ R, if x+5 ≤ y+2 then x ≤ y. Prove by contradiction For ∀x,y ∈ R, if xy< 4 then x<2 or y<2.
QUESTION 1 Expand the quotient by partial fractions. 4x +4 (x - 5)(x - 2) 8 + X-5 X-2 8 -4. X-5 (x - 5)(x - 2) 8 HA + X-5 X-2 24 12 X-5 X-2 +
3) Find the limit and prove it using definition lim 4x² + 13 x 70 x² + xt I
Prove that x4 + 3x + 4x² + 8x + 11 is irreducible in Q[x] . Make sure to completely justify all your claims.
Prove that the polynomial 9x^4 + 4x^2 − 3x + 7 is irreducible in Q[x].
5. Is f continuous at f(1)? (10 points) [-x2 +1, 4x, f(x) = -5, -1<x<0 0<x<1 x=1 1<x<3 3<x<5 - 4x + 8 1,
8. Use mathematical induction to prove that F4? = FmFn+1 Yn> 1, where Fn is the n-th Fibonacci number. k=1
The most stable nucleus in terms of binding energy per nucleon is ⁵⁶Fe. If the atomic mass of ⁵⁶Fe is 55.9349 amu, calculate the binding energy per nucleon for ⁵⁶Fe. The mass of a hydrogen atom is 1.0078 amu, and the mass of a neutron is 1.0087 amu. (1 J = 1 kg・m²/s², 1 amu = 1.66 × 10⁻²⁷ kg)
Question 13 Determine the domain of f(x)= x2 - 4x +3 x-1 in interval notation. Question 14 Given that f(x) = - 4x + 3 is a one-to-one function. Determine f-'(x).