1. Simplify by rationalizing the denominator, 2+23 /128

2. Determine the slope of the tangent to the curve at a given value of x, = 5 1, = 2

3. Consider() = {|1| /1, 1

0, = 1 .

a. Determine whether lim()exists

1

b. Sketch the graph of() and identify any points of discontinuity.

4. 4. Find the slope of, in simplified form, given(1,1)(1 +,(1 +)), where() =²

5. What is a normal to the graph of a function? Determine the equation of the normal to the graph of = 3/ ² 4 /³,(1, 7).

6. 6. Determine the slope of a tangent to() = 2( + 1)³ (² + 2 + 1)² =2. Explain how to find the equation of the normal at =2

7. A spaceship approaching touchdown on a distant planet has height h, in meters, at time t, in seconds, given by = 25² 100 + 100. When does the spaceship land on the surface? With what speed does it land (assuming it descends vertically)?

8. . Suppose that the temperature, in degree Celsius, varies with the height, in kilometers, above Earth's surface according to the equation() = 60/+2. Find the rate of change in temperature with respect to height at a height of 3 km