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From 9-17 answer explanation

 Suppose that imit as (x to infinity) f(x) = infinity and imit as (x to infinity) g(x) =-infinity . Then always,

(A) imit as (x to infinity) f(x)*g(x) = infinity

(B) imit as (x to infinity) f(x)*g(x) =-infinity

(C) imit as (x to infinity) f(x)+g(x) = infinity

(D) imit as (x to infinity) [f(x)]/[g(x)] = infinity

 Suppose that imit as (x to infinity) f(x) = infinity and imit as (x to infinity) g(x) = 0 . Then always,

(A) imit as (x to infinity) f(x)*g(x) = infinity

(B) imit as (x to infinity) f(x)*g(x) = 0

(C) imit as (x to infinity) f(x)-g(x) = infinity

(D) imit as (x to infinity) [f(x)]/[g(x)] = infinity .

 Suppose that imit as (x to a) f(x) = infinity . Then,

(A) imit as (x to a) 1/[f(x)] = infinity

(B) imit as (x to a) 1/[f(x)] = 0

(C) imit as (x to a) 1/[f(x)] =-infinity

(D) none of the above.

 Suppose that imit as (x to infinity) f(x) = 0 but (x) > 0 . Then,

(A) imit as (x to infinity) 1/[f(x)] = infinity

(B) imit as (x to infinity) 1/[f(x)] =-infinity

(C) imit as (x to infinity) 1/[f(x)] = 0

(D) imit as (x to infinity) 1/[f(x)] < 0 .

 The function (x) assumes only two values: and . No matter how big is, there is some > N such that (x) = 5 and there is some > N such that (x) = 7 . We conclude that

(A) imit as (x to infinity) f(x) = 5

(B) imit as (x to infinity) f(x) = 7

(C) imit as (x to infinity) f(x) = 6

(D) imit as (x to infinity) f(x) does not exist.

 Let (x) = 1/[x^2] . In order to ensure that (x) > N , it is enough to require that

(A) > N

(B) < N

(C) < 1/[root(N)]

(D) x| < 1/[root(N)] .

 Which of the statements is true?

(A) imit as (t to infinity) sin t = 1

(B) imit as (t to infinity) sin t = pi

(C) imit as (t to infinity) sin t = infinity

(D) imit as (t to infinity) sin t does not exist.

 Which of the statements is true?

(A) imit as (t to infinity) cos 1/t = 1

(B) imit as (t to infinity) cos 1/t = pi

(C) imit as (t to infinity) cos 1/t = infinity

(D) imit as (t to infinity) cos 1/t 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) imit as (x to 0^+) ln x , (b) imit as (x to 0^+) 1/x , (c) imit as (x to 0^-) 1/x , (d) imit as (x to 0) 1/x , (e) imit as (x to 0^+) 1/[x^2] , (f) imit as (x to 0^-) 1/[x^2] , (g) imit as (x to 0^-) cot x , (h) imit as (x to 0^+) cot x , (i) imit as (x to 0) cot x .

 Use algebra and limits laws to find the limits:

(a) imit as (x to infinity) [x+1]/[x-2] ,

(b) imit as (x to-infinity) [x^2+1]/[x^2-5]

(d) imit as (x to-infinity) [x^3+1]/[x^2+2] .

Check your answers by graphing the functions.

 Use algebra and limits laws to find the limits: (a) imit as (x to infinity) (root (x+1)-root(x)) , (b) imit as (x to infinity) (x^3-x^2) . Check your answers by graphing the functions, for example: graph = root (x+1)-root(x) for leq x leq 10000 . You may leave the -range blank.

 Find the horizontal and vertical asymptotes of (x) = [x^2-3]/[x^2-1] .

 Find the horizontal and vertical asymptotes of (x) = [x+1]/[x^2-5] .

 Find the limit imit as (x to infinity) root ([12 x^3-4 x+1]/[1+3 x+2 x^3]) .

 Let Does ttp://calculus.sfsu.edu/latexrender/pictures/3532ffa24f64b217f9c5cc798527fe67.png does have a limit as to infinity ? Explain your answer.

 Let Does ttp://calculus.sfsu.edu/latexrender/pictures/3c3289fb5e863ecb2ce878f9d3756d27.png does have a limit as to infinity ? 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 ).