Judd Quantitative Tutorial Test

 
Problem Statement

{2,4,6,8}
eval pow(8, 2)
eval 64+.002
eval 64+.001
eval 64+.0005
eval 64+.0001
eval round((sqrt(64.002)-8)/(64.002-64),7)
eval round((sqrt(64.001)-8)/(64.001-64),7)
eval round((sqrt(64.0005)-8)/(64.0005-64),7)
eval round((sqrt(64.0001)-8)/(64.0001-64),7)
eval round(1/(2*8),4)

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

 
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, xc+) and a second table of values of f(x) for x close to c but less than c (that is, xc–). 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 64 and f(x) is .

Question Sequence

Question 1

Complete the table of values of f(x) as x64+. (Round your answers to seven decimal places.)

x f(x)
64.002 0.0624995
64.001
64.0005
64.0001
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 2

As x64+, f(x) approaches (rounded to four decimal places)

2
No. What number does f(x) appear to approach as x approaches 64 from above? Remember to round to 4 decimal places.
Incorrect. Do you see where you went wrong?
Exactly.
As xc+, f(x) approaches:

 
Step 2

Question 1

Since both tables indicate convergence to the same number 0.0625 as x approaches 64 from the left and from the right, then 0.0625 is an estimate for the limit and we write

= .

2
No. What number did you find that f(x) approached as x approached 64 from above and below?
Incorrect. Do you see where you went wrong?
Excellent work.
Final estimate of the limit of f(x)

 
Demo step

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

Question Sequence

Question 4

This is a simple multiple choice question. All you need here is a query and metadata to define the feedback

A.
B.
C.

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

Question 5

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

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

Question 6

This is a more complex question, which includes -in blanks and menus.

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