Chapter 1. RogaCalcET2 2.5.013.Tutorial.SA.

1.1 Problem Statement

eval rand(5,9);

$a+1;

$b*$a-$a;

$a*$a;

2*$C1;

eval $b*$a+$a;

eval 2*($a+$a);

eval round($ansa/$ansb,2);

Estimate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or infinite).

1.2 Step 1

Recall the Quotient Law for evaluating limits given that and exist. If , then exists and .

Question Sequence

Question 1.1

For the given rational function , evaluate the limit of the numerator and denominator as x approaches $a.

= 1Wh3cvJ2xF4=

Incorrect.

Correct.

Question 1.2

The Quotient Law h6Q4QU2SWfOKIbur4GLV8BRt1Yk= apply. We say that is 5rEcHixAdeJONJPG1u7+MGlhGwvO3Ffr8ZOTskzRg00iFfNADxYU/lSGWsucE+q4 at x = $a.

Incorrect.

Correct.

1.3 Step 2

Question Sequence

Since the rational function has an indeterminate form of the type at x = $a, we can find an equivalent expression for the function by factoring its numerator and denominator and cancelling like factors, however, that we keep the domain of the original rational function.

Question 1.3

where z = nc1ItEz0kR4=.

Correct.

Incorrect.

Question 1.4

where w = nc1ItEz0kR4=, x ≠ $a.

Correct.

Incorrect.

1.4 Step 3

Since the limit is being evaluated as x approaches $a (meaning for all values of x near $a, but not equal to $a), we can try to evaluate by applying the Quotient Law for evaluating limits.