calc_tutorial_2_1_017

Chapter 1. Calculus Tutorial 2.017

1.1 Problem Statement

$a: eval {2,4,6,8} $a2: eval pow($a,2) sub f { my($x) = @_; return round((sqrt($x)-$a)/($x-pow($a,2)),7); } $ans: eval round(1/(2*$a),4)

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

1.2 Step 1

Question 1.1

To determine if a limit exists numerically for f(x), make a table of values of f(x) for x close to c but greater than c (that is, ) 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

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

x f(x)
var var
Cell 1 FB:*0.0624998
Cell 1 FB:*0.0624999
Cell 1 FB:*0.0625000

As , f(x) approaches

_max_tries:2 _feedback_correct: Correct. _feedback_hint: That's not right. Check your work. _feedback_incorrect: Incorrect.

1.3 Step 2

Question 1.2

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

x f(x)
var var
var FB:*0.0625002
var FB:*0.625001
var FB:*0.625000

As , f(x) approaches FB:*0.0625

_max_tries:2 _feedback_correct: Correct. _feedback_hint: That's not right. Check your work. _feedback_incorrect: Incorrect.

1.4 Step 3

Question 1.3

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

= FB:*0.0625

_max_tries:2 _feedback_correct: Correct. _feedback_hint: That's not right. Check your work. _feedback_incorrect: Incorrect.