Obtain the set of necessary and sufficient conditions for the following NLP Minimize Z = 2.x- 24x1x2 + 2x3 – 3x3 - 24x1x3 – 8x2X3 + 150

For 50 Equally spaced points in the interval of 0 ≤ x ≤ 3, find the value of: 1- f(x) = ex 2- Plot f(x) 3- Find the locations of f(x) ≥2 4- Find the values of f(x) ≥ 2

Use the big-θ theorems to find good reference functions for the following: f (n) = (2n^2 + 7) lg n + 2^n(n^3 + 4

3.8

E. Show that if an = 5n3 - 14n2 + 7n - 3, then an = Θ(n3).

Find the general solution of the system whose augmented matrix is given below. 1 -3 0 -1 OOO 0 0 0 10 X5 = 00 00 O A. X₁ x₂ = X3 is free X4= TOTO 0 -7 0 - 4 1 8 0 0 060 9 OB. x₁ = X1 X₂ is free X3 X4 is free X5 is free O C. X₁ = - x₂ = X3 is free X4= X5 is free O D. The system is inconsistent.

A manufacturer of programmable calculators is attempting to determine a reasonable free-service period for a model it will introduce shortly. The manager of product testing has indicated that the calculators have an expected life of 60 months. Assume product life can be described by an exponential distribution. T / MTBF -T / MTBF T| MTBF -т / МТВF T| MTBF -т / МТВF 0.10 0.9048 2.60 0.0743 5.10 0.0061 0.20 0.8187 2.70 0.0672 5.20 0.0055 0.30 0.7408 2.80 0.0608 5.30 0.0050 0.40 0.6703 2.90 0.0550 5.40 0.0045 0.50 0.6065 3.00 0.0498 5.50 0.0041 0.60 0.5488 3.10 0.0450 5.60 0.0037 0.70 0.4966 3.20 0.0408 5.70 0.0033 0.80 0.4493 3.30 0.0369 5.80 0.0030 0.90 0.4066 3.40 0.0334 5.90 0.0027 1.00 0.3679 3.50 0.0302 6.00 0.0025 1.10 0.3329 3.60 0.0273 6.10 0.0022 1.20 0.3012 3.70 0.0247 6.20 0.0020 1.30 0.2725 3.80 0.0224 6.30 0.0018 1.40 0.2466 3.90 0.0202 6.40 0.0017 1.50 0.2231 4.00 0.0183 6.50 0.0015 1.60 0.2019 4.10 0.0166 6.60 0.0014 1.70 0.1827 4.20 0.0150 6.70 0.0012 1.80 0.1653 4.30…