Let R be the unit disk $\left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 1 \right\}$ with (0, 0) removed. Is (0, 0) a boundary point of R? Is R open or closed?

Explain how to subtract polynomials.

There are two types of batteries in a bin. When in use, type i batteries last (in hours) an exponentially distributed time with rate

$$\lambda _ { i } , i = 1,2$$

. A battery that is randomly chosen from the bin will be a type i battery with probability

$$p _ { i } , \sum _ { i = 1 } ^ { 2 } p _ { i } = 1$$

If a randomly chosen battery is still operating after t hours of use, what is the probability that it will still be operating after an additional s hours?

Construct a difference table to predict the next term of each sequence. 17, 15, 25, 53, 105, 187, ...

Let v be the vector from initial point

$$P_1$$

to terminal point

$$P_2.$$

Write v in terms of i and j.

$$P _ { 1 } = ( - 3,4 ) , P _ { 2 } = ( 6,4 )$$

Find the directional derivative of

$$f(x, y) = x^2 + 2y^2$$

at x = 2 and y = 2 in the direction of h = 2i + 3j

Determine whether the triangle with the given side lengths is a right triangle. 8, 11, 14

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of each function.

$$f ( x ) = - 5 x ^ { 2 } + 3 x + 2$$

Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y=1/(x-2)-3

Explain why evaluating a limit along a finite number of paths does not prove the existence of a limit of a function of several variables.

Sketch each angle in standard position. -330°

If a speed moves away from you at half the speed of light and fires a rocket away from you at half the speed of light relative to the spaceship, common sense may tell you the rocket moves at the speed of light relative to you. But it doesn’t! The relativistic addition of velocities is given by

$$V = \frac { v _ { 1 } + v _ { 2 } } { 1 + \frac { v _ { 1 } v _ { 2 } } { c ^ { 2 } } }$$

Substitute 0.5c for both

$$v_1$$

and

$$v_2$$

and show that the velocity V of the rocket relative to you is 0.8c.

Use words to write 4.02.

Find the distance between a and b. $a = 126, b = 75$