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

Find the center, vertices, and foci of the ellipse with equation 4×2 + 9y2 = 36. (5 points)

Find the first six terms of the sequence. a1 = -7, an = 2 • an-1 (5 points)

Cantilever beams loaded with only gravity loads develop positive bending moments throughout the span.

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

You are considering a beam design that has dimensions of b = 14 in., h = 24 in., and d = 21.5 in. The beam is singly reinforced with all of the reinforcement in a single row. The concrete strength is 4,000 psi, and the yield strength of the reinforcement is 60,000 psi. What cross-sectional area of reinforcement is needed to achieve a strain in the reinforcement of 0.0075?

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

A beam has dimensions of b = 14 in., h = 24 in., and d = 21.5 in. and is reinforced with 5 No. 7 bars. The concrete strength is 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. Assuming the reinforcement has yielded, determine the tensile force T in the reinforcement.

A beam has dimensions of b = 14 in., h = 24 in., and d = 21.5 in. and is reinforced with 2 No. 5 bars. The concrete strength is 4,300 psi, and the yield strength of the reinforcement is 60,000 psi. Assuming the reinforcement has yielded, determine the depth to the neutral axis, c.

A beam has dimensions of b = 14 in., h = 22 in., and d = 19.5 in. and is reinforced with 3 No. 6 bars. The concrete strength is 9,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the compressive stress block is a = 0.68613 in. and the strain in the reinforcement is εs = 0.05242, determine the strength φMn for this beam. Assume the transverse reinforcement is not spirals.