Math
h2oFrom 1-8 chose the correct answer
From 9-17 answer explanation
Suppose that and . Then always,
(A)
(B)
(C)
(D)
Suppose that and . Then always,
(A)
(B)
(C)
(D) .
Suppose that . Then,
(A)
(B)
(C)
(D) none of the above.
Suppose that but . Then,
(A)
(B)
(C)
(D) .
The function assumes only two values: and . No matter how big is, there is some such that and there is some such that . We conclude that
(A)
(B)
(C)
(D) does not exist.
Let . In order to ensure that , it is enough to require that
(A)
(B)
(C)
(D) .
Which of the statements is true?
(A)
(B)
(C)
(D) does not exist.
Which of the statements is true?
(A)
(B)
(C)
(D) does not exist.
Graph the appropriate functions (first try by hand and then verify your sketches with the grapher) and then determine the infinite limits. Include small sketches. (a) , (b) , (c) , (d) , (e) , (f) , (g) , (h) , (i) .
Use algebra and limits laws to find the limits:
(a) ,
(b)
(c)
(d) .
Check your answers by graphing the functions.
Use algebra and limits laws to find the limits: (a) , (b) . Check your answers by graphing the functions, for example: graph for . You may leave the -range blank.
Find the horizontal and vertical asymptotes of .
Find the horizontal and vertical asymptotes of .
Find the limit .
Let Does does have a limit as ? Explain your answer.
Let Does does have a limit as ? Explain your answer.
The function has a limit as . This means that if is sufficiently large (that is if for some number ), the values of are closer to than a number . (a) Sketch the graph and a horizontal strip such that (if you are using the grapher, note that it has the capability to display more than one graph at once. The functions to be plotted are separated by a semincolon; you can input 1/x+3; 2.8; 3.2 for this problem). Based on the graph decide which portion of the graph is contained in the strip. That is find such that for the graph is included in the strip.
(b) For the following values of , using algebraic inequalities find such that the graph restricted to is contained in the horizontal strip ? Note that the first part of this inequality is always satisfied so it is enough to solve
for .
(c) What is a formula for ? (in terms of ).