Chapter 1. Judd Quantitative Tutorial Test

1.1 Problem Statement

{2,4,6,8}
eval pow($a, 2)
eval $a2+.002
eval $a2+.001
eval $a2+.0005
eval $a2+.0001
eval round((sqrt($p1_1)-$a)/($p1_1-$a2),7)
eval round((sqrt($p1_2)-$a)/($p1_2-$a2),7)
eval round((sqrt($p1_3)-$a)/($p1_3-$a2),7)
eval round((sqrt($p1_4)-$a)/($p1_4-$a2),7)
eval round(1/(2*$a),4)

Estimate the limit numerically or state that the limit doesn't exist. Test.

1.2 Step 1

To determine if a limit exists numerically for , make a table of values of f(x) for x close to c but greater than c (that is, x → c+) and a second table of values of f(x) for x close to c but less than c (that is, x → c–). If both tables indicate convergence to the same number L, we take L to be an estimate for the limit.

In the given problem, c is $a2 and f(x) is .

Question Sequence

Question 1.1

Complete the table of values of f(x) as x → $a2+. (Round your answers to seven decimal places.)

x f(x)
$p1_1 $p1_1_a
$p1_2 4KozdQDseRa1gpJK
$p1_3 jY3eeGkeo+oqGJ6H
$p1_4 Bd1SHbUm9tYOoTh7
2
No. Calculate f(x) for each of the values of x given in the left column, and enter those values in the right column. Remember to round to 7 decimal places.
Incorrect. See above for the correct answers, and try to work out where you went wrong before going on to the next question.
Nice job.
Values of f(x) for x = c + 0.001 / c + 0.0005 / c + 0.0001

Question 1.2

As x → $a2+, f(x) approaches qjqZz1N+poo= (rounded to four decimal places)

2
No. What number does f(x) appear to approach as x approaches $a2 from above? Remember to round to 4 decimal places.
Incorrect. Do you see where you went wrong?
Exactly.
As x → c+, f(x) approaches:

1.3 Step 2

Question 1.1

Since both tables indicate convergence to the same number $ans as x approaches $a2 from the left and from the right, then $ans is an estimate for the limit and we write

= qjqZz1N+poo= .

2
No. What number did you find that f(x) approached as x approached $a2 from above and below?
Incorrect. Do you see where you went wrong?
Excellent work.
Final estimate of the limit of f(x)

1.4 Demo step

This step is included in the template to illustrate a couple of extra things.

Question Sequence

Question 1.4

BMazM8HC8L/DSeERf50Wf8pdx7RipV8eFYERvJBS0wMeCmWF/OhU6sL6MYGluISATiljoaLkvpilg7PKMFW8sZKflSeXsAqi9yU7Xoh6G7sOoOoP2PMVbRH4h8soNANdcaWSfNpUPMXDEr3+YxOlG++A1Mt+z3XiijdyikHI+HLTFwTZYQB1VQsTWkKOcTxC3U8Myg==
2
Correct.
That's not right. Check your work.
Incorrect.

Question 1.5

This is a simple fill-in-the-blank question. What is the capital of Oregon?

vXzYERXVdXog8cNH

2
Correct.
That's not right. Check your work.
Incorrect.

Question 1.6

This is a more complex question, which includes i+gXJPH7GXE=-in blanks and EqtjiwKqDdYLdXEKkBEBEAckAWaamwky menus.

2
Correct.
That's not right. Check your work.
Incorrect.