(8) Find the infimum, minimum, maximum and supremum of each of the following sets (write d.n.e. if it does not exist). S inf S min S max S sup S {1-;\neN} {xER | x³-4x²+x+6 >0} { / - / | m, n €N} n 00 Ö|1 - 1/13 2+ n' n n=1 {XEQ | x ≤ 2}

Q: {-) Evaluate the domain of f(x)=Ven(Sx-XE)

A: The given function is f(x)=ln5x-x24

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

A:

Q: b. Маx z %3DX1 + X2 s.t. 2x1 + x2 < 20 X1 +3x2 < 15 X2 < 4 X1, X2 2 0

A:

Q: Show that if (B) (C) N N then the value of neither x nor y can exceed 1/4. (A) N = X, 2x, = 3x and…

A:

Q: TF x and y are orthon ormal rectors then Pind Value of Ilx+y12 - ||x-Y2

A:

Q: evaluate L-1 { t/(s-2)(s+3)}

A: By using partial fraction and table of Laplace transform we solve the given problem as follows :

Q: 9. Solve In (x+5) 2 2. O A. (x | x 2 12.3891} B. (x | x 2 2.3891} O C. (x |xs 12.3891} O D. {x |x s…

A: Given:         ln(x+5)≥2

Q: B.Solve the problem below. Show the complete solution. Out of the 300 grade 10 students of a certain…

A: Number of student joined mathematics club is 120. Number of student joined science club is 115.…

Q: - (10 points) Show |a – b| < |a| + [b| Va,b eR.

A: We have to show that  a-b≤a+b      ∀a, b∈ℝ

Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

A:

Q: Evaluate х3 (x* — 1)3 dx x*(x* – 1)ª + C (x* – 1)* + C 16 4x4 (x* – 1)4 (x4 – 1)4 + C 16 + C 4

A: The given integral is; Integration of x3(x4-1)3.

Q: 3.6 Error analysis of the upwind scheme We notice that the upwind scheme can be written S (1+v)U} –…

A: Error analysis of Upward scheme  To prove: Ujn+1= 1+vUjn-vUj+1n ,  if a&lt;01-vUjn+vUj-1n ,  if…

Q: Show that exp(z²)| ≤ exp(|z|²) for all - E C.

A:

Q: Let f :[-2,6] R be the function given by * if - 2sx<0 if 0sx< 2 4 -x if 2 sxs6. f(x) = 2.x For each…

A:

Q: Let f(n) and g(n) be functions satisfying  f(n) = {sqrt (n), 1 + f(n+1)} if sqrt (n) is an integer…

A: Let f(n)={n,1+f(n+1)} To find 1+f(n+1) replace n by n+1 in f(n) therefore, f(n+1)=n+1 and…

Q: Determine the interval of convergence for € (-1)" n! (x-5)" ΑΞΟ 34

A:

Q: number o such that if 0< x-1.5 <8 then x² 1 1.5²

A: We have to find largest δ such that if 0&lt;x-1.5&lt;δ then 1x2-11.52&lt;1

Q: lex. min. {g, (x), g₂ (x)} 9₁ (x): -2x1 - x₂ ≥ 9 92 (x): X₁ X1 - 2x₂ ≥ 10 st. 2x1 + 5x2 ≤ 16 6x₁ +…

A:

Q: Find the distance between the point and the line given by the set of parametric equations. (Round…

A: