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From 1-8 choice the correct answer with explain:

1. Based on this graph of = x^x ,

ttp://calculus.sfsu.edu/latexrender/pictures/0436dfda358fad50c497dfadb5f55195.png

(A) imit as (x to 0+) x^x = 1

(B) imit as (x to 0-) x^x = 1

(C) imit as (x to 0) x^x is a number slightly less than .

(D) imit as (x to 0-) x^x = 2 .

2. imit as (x to 2^-) [x^3-8]/[x-2]

(A)

(B)

(C) exists but it is equal to a number not listed here

(D) the limit does not exist since the denominator is when = 2 .

3. As to 2^- , the values of (x) approach . However, as to 2+ the values of (x) do not approach any particular number. Which of the statements is then correct?

(A) imit as (x to 2-) f(x) =-3 but neither imit as (x to 2+) f(x) nor imit as (x to 2) f(x) exists.

(B) imit as (x to 2+) f(x) =-3

(C) imit as (x to 2) f(x) =-3

(D) All above are incorrect.

4. Which of the following equations is correct ?

(A) ttp://calculus.sfsu.edu/latexrender/pictures/646f3551b02aebeaeafe408989245027.png

(B) ttp://calculus.sfsu.edu/latexrender/pictures/a9bb2d56c0608dbe1e3dcee8c6ab45f3.png

(C) imit as (h to 0) [h^2]/h = limit as (h to 0) h = 0.

(D) Since the denominator goes to zero, all the above equations are not correct.

5. Let

ttp://calculus.sfsu.edu/latexrender/pictures/ef6733addb5f921ba7abc63fc980f29a.png

(A) imit as (x to-1^-) f(x) =-1/2 and imit as (x to-1^+) f(x) =-2

(B) imit as (x to-1^-) f(x) =-2 and imit as (x to-1^+) f(x) =-1/2

(C) imit as (x to-1^-) f(x) does not exist and imit as (x to-1^+) f(x) does not exist

(D) imit as (x to-1^-) f(x) = 1 and imit as (x to-1^+) f(x) = 1

6. (A) imit as (x to 1) [x^2-x+1]/[x+1] = 1/2

(B) imit as (x to 1) [x^2-x+1]/[x+1] does not exist

(C) imit as (x to 1) [x^2-x+1]/[x+1] cannot be calculated since ^2-x+1 does not factor

(D) none of the aboove.

7. Based on this graph of = f(x) we conclude that

ttp://calculus.sfsu.edu/latexrender/pictures/1c16b49e4fc4262db8e28669d9b8ec59.png

(A) imit as (x to 0) f(x) = 1

(B) imit as (x to 0) f(x) = 0

(C) imit as (x to 0) f(x) does not exist

(D) imit as (x to 0) f(x) = 0 or imit as (x to 0) f(x) = 1 .

8. Based on this graph of = f(x) we conclude that

ttp://calculus.sfsu.edu/latexrender/pictures/a0dd26a2ea8d23f1e82bbec067e20987.png

(A) imit as (x to 2^-) f(x) = 3

(B) imit as (x to 2^-) f(x) = 2

(C) imit as (x to 2^-) f(x) does not exist

(D) imit as (x to 2^-) f(x) = 1 .

 Find the limits (a) imit as (x to 0^-) 2 x , (b) imit as (x to 3^+) x , (c) imit as (x to 3^+) 5 , (d) imit as (x to-1^-) |x+2| ? In each case if you use a limit law, mention which one you are using.

 Sketch by hand the graph of the function

ttp://calculus.sfsu.edu/latexrender/pictures/a68047785939337fef71702224fc64d6.png

Find imit as (x to-1^-) f(x) . Find imit as (x to-1^+) f(x) . Are these two limits the same? What can you say about imit as (x to-1) f(x) ?

 Use the Limit Laws to find the limit. Graph each function before you submit the solution to check if the graph supports your conclusion. No need to include the graph though. imit as (x to 3) (x^2-x+2) .

 Use the Limit Laws to find the limit imit as (x to 3) (x^2-x+2/x^3) . [Note: ^2-x+2/x^3 not = [x^2-x+2]/[x^3] .

 Use the Limit Laws to find the limit imit as (x to-3) [x^2-9]/[x+3] .

 Use the Limit Laws to find the limit imit as (x to 7) [root(x)-root(7)]/[x-7]

 Use the Limit Laws to find the limit imit as (x to 5) [x^3-125]/[x-5]

 Does the limit imit as (x to 1) [x^2-x-1]/[x-1] exist?

 Use Limit Laws to find the limit imit as (x to 1) [x^2+x-2]/[x-1] .

 Graph the function ttp://calculus.sfsu.edu/latexrender/pictures/395233185785178555ba1ed6fc354ffa.png where 0.2 leq x leq 0.2 . Then graph (x) where varies over a smaller interval, for example, .06 leq x leq 0.06 . Determine imit as (x to 0) sin [pi]/x if it exists. Describe in a paragraph the behavior of the values of (x) near = 0 . Include graphs in your solutions.

 Graph the function ttp://calculus.sfsu.edu/latexrender/pictures/82f07f5bedaf6d5c33fadb7f2d16afe4.png

Then graph (x) where varies over a smaller interval, for example, .08 leq x leq 0.08 . Describe in a paragraph the behavior of the values of (x) near = 0 . The video on the margin might help. Based on this video what are the two functions lue g(x) and reen h(x) squeezing ed f(x) , that is such that reen h(x) black leq red f(x) black leq blue g(x) ? What is imit as (x to 0) green h(x) ? and what is imit as (x to 0) blue g(x) ? Determine imit as (x to 0) red x^2 sin [pi]/x if it exists. Include graphs in your solutions.

 Discuss on the forum but do not submit. Let (x) be the smallest digit that appears in the decimal expansion of . For example, (0.123123123123 dots) = 0 and (1.1111 dots) = 1 , and (2.10101010101 dots) = 0 . Find if they exist these limits: (a) imit as (x to 1) f(x) , (b) imit as (x to 2) f(x) ?

 Discuss on the forum but do not submit. We define on a colored interval 0,1) .

(a) Determine in the case when the entire interval is blue? (b) Determine in the case when the entire interval is black? (c) Does there exist if near (in every neighborhood of ) there are numbers colored blue and there are numbers colored black? Hand sketch a possible graph of .