1922 Guess the value of the limit (if it exists) by evaluating the function at the given

Explain in your own words what is meant by the equation Is it possible for this statement to be true and yet ? Explain

Explain what it means to say that and In this situation is it possible that exists? Explain.

Explain the meaning of each of the following.

Use the given graph of to state the value of each quantity, if it exists. If it does not exist, explain why. (a) (b) (c) (d) (

For the function whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why. (a) (b) (c) (d) (e)

For the function whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why. (a) lim (b) (c) xl3 hx lim xl3 hx lim xl3 hx h li xl0 lim hx xl0 h3 hx 2.2 Ex lim h0 hx xl0 hx xl5 lim hx xl5 h2 hx lim x

For the function whose graph is given, state the value of each quantity, if it exists. If it does not exist, explain why.lim tt tl0 lim tt tl0 tt t y lim tt tl2 lim tt tl2 tt lim t t2 tt lim

For the function whose graph is shown, state the following. (a) (b) (c) (d) (e) The equations of the vertical asymptotes. x y _3 0 2 5 lim xl3 lim Rx xl3 Rx lim xl5 lim Rx x l

For the function whose graph is shown, state the following

A patient receives a 150-mg injection of a drug every 4 hours. The graph shows the amount of the drug in the blood stream after hours. Find and and explain the significance of these one-sided limits

1112 Sketch the graph of the function and use it to determine the values of for which exists. fx  1  x x 2 2  x if x  1 if 1 x  1 if x  1 a

1112 Sketch the graph of the function and use it to determine the values of for which exists.fx  1  sin x cos x sin x if x  0 if 0 x if x  fx

1314 Use the graph of the function to state the value of each limit, if it exists. If it does not exist, explain why.fx 1 1  e 1x f

1314 Use the graph of the function to state the value of each limit, if it exists. If it does not exist, explain why.fx x 2  x sx 3  x 2 li

1518 Sketch the graph of an example of a function that satisfies all of the given conditions.lim f 0 1 xl0 lim fx 2 xl0 f x 1 97909_02_

1518 Sketch the graph of an example of a function that satisfies all of the given conditions.xl3 lim f x 2 xl3 lim fx 2 xl0 fx 1 f0 1 f3 1 lim x

1518 Sketch the graph of an example of a function that satisfies all of the given conditions.lim f x 2 xl3 lim fx 2 xl3 f x 4 f0 1 f3f 3 3 f2 1 lim x

1518 Sketch the graph of an example of a function that satisfies all of the given conditions.xl4 lim fx 3 xl0 lim fx 0 xl0 f x 2 f 3 3 flim f0 2 f4 1 xl4 f x 0 lim xl4

1922 Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim xl2 x 2  2x x 2  x  2 x 2.5, 2.1, 2.05, 2.01, 2.005, 2.001, l 1.9, 1.95, 1.99, 1.995, 1.999

1922 Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim xl  1 x 2  2x x 2  x  2 x 0, 0.5, 0.9, 0.95, 0.99, 0.999, l 2, 1.5, 1.1, 1.01, 1.001

1922 Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim t 0.5 0.1 0.01 0.001 0.0001 tl0 e5t 

1922 Guess the value of the limit (if it exists) by evaluating the function at the given numbers (correct to six decimal places).lim hl0 2  h 5  32 h l h 0.5 0.1 0.01 0.001 0.0001 lim h

2326 Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.lim xl0 sx  4  2 x

2326 Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.im xl0 tan 3x tan 5x

2326 Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.lim xl1 x6  1 x10  1

2326 Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.lim xl0 9x  5x x

(a) By graphing the function and zooming in toward the point where the graph crosses the -axis, estimate the value of . (b) Check your answer in part (a) by evaluating for values of that approach 0.

(a) Estimate the value of by graphing the function . State your answer correct to two decimal places. (b) Check your answer in part (a) by evaluating for values of that approach 0

2937 Determine the infinite limit.lim xl3 x  2 x  3

2937 Determine the infinite limit.im xl3 x  2 x  3

2937 Determine the infinite limit.lim xl1 2  x x  1 2 l

2937 Determine the infinite limit.lim xl5 e x x  5 3 li

2937 Determine the infinite limit.lim cot x xl3 lnx 2  9 l

2937 Determine the infinite limit.lim xl l

2937 Determine the infinite limit.lim xl 2 x csc x

2937 Determine the infinite limit.lim xl 2 x 2  2x x 2  4x  4

2937 Determine the infinite limit.lim xl2 x 2  2x  8 x 2  5x  6

(a) Find the vertical asymptotes of the function ; (b) Confirm your answer to part (a) by graphing the function

Determine and (a) by evaluating for values of that approach 1 from the left and from the right, (b) by reasoning as in Example 9, and ; (c) from a graph of

. (a) By graphing the function and zooming in toward the point where the graph crosses the y-axis, estimate the value of . (b) Check your answer in part (a) by evaluating for values of x that approach 0

(a) Estimate the value of the limit to five decimal places. Does this number look familiar? ; (b) Illustrate part (a) by graphing the function

. (a) Graph the function for . Do you think the graph is an accurate representation of ? (b) How would you get a graph that represents better?

. (a) Evaluate the function for 1, 0.8, 0.6, 0.4, 0.2, 0.1, and 0.05, and guess the value of (b) Evaluate for 0.04, 0.02, 0.01, 0.005, 0.003, and 0.001. Guess again.

(a) Evaluate for , 0.5, 0.1, 0.05, 0.01, and 0.005. (b) Guess the value of . (c) Evaluate for successively smaller values of until you finally reach a value of for . Are you still confi- dent that your guess in part (b) is correct? Explain why you eventually obtained 0 values. (In Section 4.4 a method for evaluating the limit will be explained.) ; (d) Graph the function h in the viewing rectangle by . Then zoom in toward the point where the graph crosses the y-axis to estimate the limit of as x approaches 0. Continue to zoom in until you observe distortions in the graph of h. Compare with the results of part (c).

Graph the function of Example 4 in the viewing rectangle by . Then zoom in toward the origin several times. Comment on the behavior of this function.