M161- Survey of Calculus Section 09 Exam 1 Name:________________________________________ No calculators. You must show all work for full credit. 1. (2 points each) Evaluate the following limits using the graph above: a. b. c. d. e. f. (3 points) Is continuous. continuous at ? Explain why or why not using the definition of g. (3 points) Is continuous. continuous at ? Explain why or why not using the definition of 2. (4 points each) Find each of the following limits, or state that it does not exist. a. b. c. d. e. 3. (15 points) a. Use the limit definition of the derivative to find the derivative of b. Find the slope of the line tangent to c. Write the equation of the line tangent to at the point at the point . . 4. (5 points each)Find the derivative of each function (don’t simplify all the way). a. b. c. d. 5. (9 points) Find the second derivative of 6. (10 points) Use implicit differentiation to find of 7. (10 points) On Halloween night, Charlie Brown’s friend Linus is waiting in the local pumpkin patch to catch the Great Pumpkin as it rises from the pumpkin patch to bring all good calculus students candy. He spots the Great Pumpkin 12 feet away, just as it is starting to rise. If the pumpkin is rising at a rate of 3 feet per minute, how fast is the distance between the pumpkin and Linus changing when it has risen 5 feet off the ground?