1. (a)

1. (a)

1. (a)

1. (a)

1. (8 points) The half-life of cesium

1. (8 points) The half-life of cesium

1. (7) y = 3 sinx, y = sin 2x, − π 2 ≤ x ≤ π 2 . sol: A = ∫ π/2 |sin2x

1. (7) y = 3 sinx, y = sin 2x, − π 2 ≤ x ≤ π 2 . sol: A = ∫ π/2 |sin2x

1. (7 Points) Suppose that y = f(x) is a differentiable function on

1. (7 Points) Suppose that y = f(x) is a differentiable function on

1. (6x + 3) + (2x - 7) 2. (9m - 1) + (2m² - 4) 3. (-4p²

1. (6x + 3) + (2x - 7) 2. (9m - 1) + (2m² - 4) 3. (-4p²

1. (6pts) Find the nth-degree polynomial function with real

1. (6pts) Find the nth-degree polynomial function with real

1. (6%) f(x, y, z) = ln(xy + z). (1,2,1) (1,2,1). sol: ∂f ∂y (1,2,1) = 1 xy +

1. (6%) f(x, y, z) = ln(xy + z). (1,2,1) (1,2,1). sol: ∂f ∂y (1,2,1) = 1 xy +

1. (6 points)For the function whose graph is given, arrange the

1. (6 points)For the function whose graph is given, arrange the

1. (5) Simplify: 2. (5) Solve: and 1)2( . Write the solution in interval

1. (5) Simplify: 2. (5) Solve: and 1)2( . Write the solution in interval

1. (4 pts) Calculate the formal charge on each C, O, and N in the

1. (4 pts) Calculate the formal charge on each C, O, and N in the

1. (4 ) 2. Solve 16 = 64 3. Simplify 32 4. Evaluate 5. Write in

1. (4 ) 2. Solve 16 = 64 3. Simplify 32 4. Evaluate 5. Write in

1. (31 points) Suppose that the following definitions have been

1. (31 points) Suppose that the following definitions have been

1. (3 - 2i) + (14 – 5i) 2. (-5 + 6i) – (13 – 2i) 3. (3 – 5i)2 4. (12 + 4i)(7

1. (3 - 2i) + (14 – 5i) 2. (-5 + 6i) – (13 – 2i) 3. (3 – 5i)2 4. (12 + 4i)(7

1. (20pts) (Image projection ) Consider the cube with points P1, P2

1. (20pts) (Image projection ) Consider the cube with points P1, P2

1. (20%) One mole of N2 gas is contained at 273 K and a pressure

1. (20%) One mole of N2 gas is contained at 273 K and a pressure

1. (20%) Consider two coupling harmonic oscillators with the same

1. (20%) Consider two coupling harmonic oscillators with the same

1. (20 pts) Let V = span(e x,e−x, xex, xe−x) be a subspace of C

1. (20 pts) Let V = span(e x,e−x, xex, xe−x) be a subspace of C

1. (20 points total, 5 pts each) Which of the following are true and

1. (20 points total, 5 pts each) Which of the following are true and

1. (2 points each) Write your answer in the box to the right of

1. (2 points each) Write your answer in the box to the right of

1. (18%) Evaluate the limits (a) lim (ex − 1) sol. Let f(x)=(e x − 1

1. (18%) Evaluate the limits (a) lim (ex − 1) sol. Let f(x)=(e x − 1

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