Find the limit of the function by using direct substitution. (6 points)  

A beam has dimensions of b = 14 in., h = 28 in., d’ = 2.5 in., and d = 25.5 in. It is reinforced with 2 No. 5 bars on the compression side and 5 No. 8 bars on the tension side. The concrete strength is 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.588 in., determine the strain in the compression reinforcement, ε’s.

Determine β1 given that f’c = 8,500 psi.

Find the derivative of f(x) = at x = 11. (5 points)

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. B = 46°, a = 12, b = 11 (5 points)

Let u = , v = . Find -4u + 2v. (5 points)

A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 19 feet and the height from the ground to the front doors is 4 feet, how long is the ramp? (Round to the nearest tenth.) (5 points)

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -1 – 3 sin θ (5 points)

Express the complex number in trigonometric form. 4i (5 points)

Determine whether the sequence converges or diverges. If it converges, give the limit. 48, 12, 3, , …  (7 points)