One-Sided Limits Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Sketch the graph of the function one sided limits homework _gr_1.gif] .

and then use the graph to determine which the following statements about the function are true and which are false?

        (a)

        (b) does not exist

        (c)

        (d)

        (e)

        (f) does not exist

        (g)

        (h) exists at every in the open interval

        (i) exists at every in the open interval

        (j)

        (k) does not exist

(2) Sketch the graph of the function one sided limits homework _gr_18.gif] .

and then use the graph to determine the following?

        (a) and

        (b) Does exist? If so, what is it? If not, why not?

        (c) Find and

        (d) Does exist? If so, what is it? If not, why not?

(3) Let Use the graph of to determine the following,

one sided limits homework _gr_28.gif]

    (a) Does exist? If so, what is it? If not, why not?

    (b) Does exist? If so, what is it? If not, why not?

    (c) Does exist? If so, what is it? If not, why not?

(4) Graph Find and Does exist? If so, what is it? If not, why not?

(5) Graph Find and Does exist? If so, what is it? If not, why not?

(6) Graph one sided limits homework _gr_40.gif]

    (a) What is the domain and range of

    (b) At what points if any does exist?

    (c) At what points does only the left-hand limit exist?

    (d) At what points does only the right-hand limit exist?