Chapter 3.1, Problem 4E

Consider the sequence below: 1 1 1 (a) Express this sequence as a recurrence relation (b) Express this sequence in the form {a}=1 (c) Does this sequence converge or diverge? Justify your answer. Consider the sequence below: 1 1 1 1, 4' 9' 16' (a) Express this sequence in the form {ak}=1 (b) Does this sequence converge or diverge? Justify your answer. Consider the sequence below: 345 2. 4' 9' 16' ·} (a) Express this sequence in the form {a}1 (b) Does this sequence converge or diverge? Justify your answer.

Let M = M₁U M₂ UM3 and K M₁ = {(x1, x2) ER²: 2 ≤ x ≤ 8, 2≤ x ≤8}, M₂ = {(x1, x2)™ € R² : 4 ≤ x₁ ≤ 6, 0 ≤ x2 ≤ 10}, M3 = {(x1, x2) Є R²: 0 ≤ x₁ ≤ 10, 4≤ x ≤ 6}, ¯ = cone {(1, 2), (1,3)†} ≤ R². (a) Determine the set E(M,K) of efficient points of M with respect to K. (b) Determine the set P(M, K) of properly efficient points of M with respect to K.

5.17 An aluminum curtain wall panel 12 feet high is attached to large concrete columns (top and bottom) when the temperature is 65°F. No provision is made for differen- tial thermal movement vertically. Because of insulation between them, the sun heats up the wall panel to 120°F but the column to only 80°F. Determine the consequent compressive stress in the curtain wall. CONCRETE COLUMNS CONNECTIONS Stress= ALUMINUM WALL PANEL 12'-0"

Use the growth rate of sequences theorem to find the limit or state it diverges

6.2 יך 4" 2" 2" Find the centroid of the following cross-sections and planes. X= Y=

Find the directional derivative of the function at P in direction V

6.4 49 Find the centroid of the following cross-sections and planes. X=_ Y= C15 XAO (CENTERED) KW14x90

calculate the maximum value of the directional derivative

5.18 The steel rails of a continuous, straight railroad track are each 60 feet long and are laid with spaces be- tween their ends of 0.25 inch at 70°F. a. At what temperature will the rails touch end to end? b. What compressive stress will be produced in the rails if the temperature rises to 150°F? T= Stress= L= 60' 25 @T=70°F