Math 151 WIR Night- before- Exam 1 Drill

Section 1.1

1. Find the unit vector which has the same direction as the vector from P(2, -1) to Q(1, 4).

2. Sketch a quadrilateral and label the sides counterclockwise as vectors a, b, c, and d. Describe each diagonal as a vector in terms of one or more of the side vectors.

3. A box is held in place by a cable on a ramp which makes an angle of 60 degrees to the horizontal.

If the mass of the box is 50kg, find the magnitude of the tension in the cable.

Section 1.2

1. Given the points A(-1,2), B(2,1) and C(0,5), find angle ACB.

2. Let a=-2i+3j and b=<1, 2>. Find the vector projection of b onto a.

3. A 10 kg suitcase sits at the top of the ramp of a cruise ship which is 4 meters tall and has a horizontal base of 2 meters. Assuming no friction, find the work done by gravity when the suitcase slides from the top of the ramp to the bottom.

Section 1.3

1.a) Find parametric equations for the line passing through the points (2, -3) and

(1, 2) so that x(0)=2 and y(0)=-3.

b) Find a vector equation for the line that passes through (3, 7) and is perpendicular to the line in a.

2. A cannonball is fired from a cannon. The path of the ball is given by the parametric equations

and (x and y are in feet). Determine how far away from the cannon the ball will strike the ground.

3. Describe the motion of a particle if the position of the particle is given by x=3sin(t) and y=-2cos(t),.

4. Find the distance from the point P(2, 5) to the line:

a) with parametric equations x(t) = 4t - 6 y(t) = -3t+7

b) with vector equation r(t) = (1+2t)i + (4-9t)j

Section 2.2

1. Compute each limit or show it does not exist.

a)

b)

c)

Section 2.3

1. Compute each limit or show it does not exist:

a)

b)

c)

d)

Section 2.5

1. Given Determine whether f is continuous at x=5 from the left, right, both or neither.

2. Find the value of c which makes f(x) continuous.

3. Find an integer N so that has a solution in the interval [N, N+1].

Section 2.6

1. Compute the following limits:

a)

b)

c)

Section 2.7

1. The position of a particle moving along the x axis is given by the function , where s is in meters and t is in seconds. Compute the average velocity of the particle over the interval [0, 2].

2. Given the curve , use the limit definition to find a vector tangent to the curve and parametric equations for the line tangent to the curve at the point (-2,4).

3. Use the limit definition to find the slope and equation of the line tangent to the curve at the point where x=5.

Section 3.1

1. Use the limit definition to find the derivative of .

2. Given , determine whether f is continuous and/or differentiable at x=0.

3. Find A and B so that f is differentiable for all x.

4. Find all x values where f has no derivative.

Section 3.2

1. Find the derivative of .

2. Find the derivative of

3. Let f and g be differentiable functions such that f(2)=6, f'(2)=2, g(2)= -3, and g'(2)=5.

Find the equation of the tangent line to h=fg at the point where x=2.

4. Find the x-coordinates of the points on the graph of where the tangent line passes through the point (2, 5).

5. p(1)=3, p'(1)= -1 Find the equation of the tangent line to f at (1, f(1)).