Chapter 2, Problem 9CR

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

Strength of Materials Problems 5.16 A long concrete bearing wall has vertical expansion joints placed every 40 feet. Determine the required width of the gap in a joint if it is wide open at 20°F and just barely closed at 80°F. Assume α = 6 × 10-6/°F. Width= CONCRETE BEARING WALL EXPANSION JOINT 40' 40' 40' 293

2) If Mand N be two water hyper Plane ofx Show that MUN and MN is hy Per Plane ofx with prove and Examplame. or 3) IS AUB is convex set and affine set or blensed set or symmetre setorsubsie.... Show that A and B is convex or affine or Hensedsed or symmetivce or subspace. 4) 18 MUN is independence show that Prove or ExPlane Mand Nave independend. or not. 5) Jet X be Vector Pace over I show that is xty tnx st Xty 3 fix→ F s-t f(x) (9) Jet Mand N be two blanced set of Xbe Vector space show tha MUNIS ansed set

Can you show me a step by step explanation please.