Chapter 1. Working with Data
Working with Data
1.1 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.
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 16 and f(x) is .
1.3 Step 2
Question 1.3
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)
1.4 Demo step
This step is included in the template to illustrate a couple of extra things.