Chapter 1. calc_tutorial_14_8_011

 
Problem Statement

{2,4,6,8}
eval pow(4, 2)
eval 16+.002
eval 16+.001
eval 16+.0005
eval 16+.0001
eval round((sqrt(16.002)-4)/(16.002-16),7)
eval round((sqrt(16.001)-4)/(16.001-16),7)
eval round((sqrt(16.0005)-4)/(16.0005-16),7)
eval round((sqrt(16.0001)-4)/(16.0001-16),7)
eval round(1/(2*4),4)

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

 
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 16 and f(x) is .

Question Sequence

Question 1

Complete the table of values of f(x) as x → 16+. (Round your answers to seven decimal places.)

x f(x)
16.002 0.1249961
16.001
16.0005
16.0001
_max_tries:2 _feedback_incorrect_first: 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. _feedback_incorrect: Incorrect. See above for the correct answers, and try to work out where you went wrong before going on to the next question. _feedback_correct: Nice job. _question_report_text: Values of f(x) for x = c + 0.001 / c + 0.0005 / c + 0.0001

 
Step 2

Question 3

Since both tables indicate convergence to the same number 0.1250 as x approaches 16 from the left and from the right, then 0.1250 is an estimate for the limit and we write

= .

_max_tries:2 _feedback_incorrect_first: No. What number did you find that f(x) approached as x approached 16 from above and below? _feedback_incorrect: Incorrect. Do you see where you went wrong? _feedback_correct: Excellent work. _question_report_text: 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.
_max_tries:2 _feedback_correct: Correct. _feedback_hint: That's not right. Check your work. _feedback_incorrect: Incorrect.