Stewart_Calc_7ET ch02sec02
MULTIPLE CHOICE
1. Estimate the value of the following limit by graphing the function .
Round your answer correct to two decimal places.
a.
b.
c.
d.
3.18
e.
2. Use the graph of the function to state the value of if it exists.
a.
b.
1
c.
d.
e.
does not exist
3. Use the graph of the function to state the value of , if it exists.
a.
b.
c.
d.
e.
does not exist
4. Sketch the graph of the function f and evaluate
a.
1
c.
3
b.
d.
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
3
1
5. Sketch the graph of the function f and evaluate
a.
Does not exist
c.
Does not exist
b.
d.
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
2
5
6. Use the graph of to guess at the limit , if it exists.
a.
3
b.
Does not exist
c.
2
d.
1
NUMERIC RESPONSE
1. Evaluate the function
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
at the given numbers (correct to six decimal places). Use the results to guess the value of the
limit
2. By graphing the function
and zooming in toward the point where the graph crosses the y-axis, estimate the value of
3. Consider the following function.
Determine the values of a for which exists.
4. How close to 2 do we have to take x so that is within a distance of 0.01 from 13?
5. Find the vertical asymptotes of the function.
SHORT ANSWER
1. Use the graph of the function to find each limit.
, ,
2. Use the graph of the function to find each limit.
, ,
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
1 2 3 4 5–1–2–3–4–5 x
1
2
3
4
5
–1
–2
–3
–4
–5
y
3. Complete the table by computing at the given values of x, accurate to five decimal
places. Use the results to guess at the indicated limit, if it exists, to three decimal places.
x
4. Complete the table by computing at the given values of x, accurate to five decimal
places. Use the results to guess at the indicated limit, if it exists, to three decimal places.
x
4.9
4.99
4.999
5.001
5.01
5.1
x
4.9
4.99
4.999
5.001
5.01
5.1
0.1
0.1
5. Complete the table by computing at the given values of x, accurate to five decimal
places. Use the results to guess at the indicated limit, if it exists, to three decimal places.
x
