Math 151 Test 2 Print Name Time: 9, 10, 12

Recall that the slope of the tangent line for at a point is defined to be

1. If

1. Use the definition to find the slope of the tangent line at

2. Find the tangent line equation at

2. Consider , interpret it as the slope of the tangent line for a function at a point. You need to identify the function and the point.

3. If

1. find by showing your work,

2. determine if is continuus at explain.

3. sketch the graph of

4. If Then use the squeezing principle to find the limit of [Specify two functions when applying the squeezing principle.]

5. Let

1. Determine the value so that the function is continuous everywhere.

2. Sketch the function after you find your answer for the number

6. Define a function , whose graph is similar to the function, and satisfies ALL the following conditions:

1. the period of is

2. the function has amplitude of

3. the function has a maximum at

7. Explain why graphically.