# Chapter 1. RogaCalcET2 2.5.013.Tutorial.SA.

## 1.1Problem 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).

## 1.2Step 1

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

### Question 1.1

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

= 1Wh3cvJ2xF4=

= 1Wh3cvJ2xF4=

Incorrect.
Correct.

### Question 1.2

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

Incorrect.
Correct.

## 1.3Step 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.

## 1.4Step 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.

### Question 1.5

Evaluate the limit of the numerator and denominator as x approaches \$a.

= BXETLrOxfxWcrhv0

= WDGIqOk3EfJe+Vr/

Correct.
Incorrect.

### Question 1.6

Thus, the Quotient Law PXcxRRPwVznkzmRiLdM8PZPj3qw= apply to and the limit G3WoGiusd49jA3XEAg63iCp80mVMXfEpMr/LxQ==.

Correct.
Incorrect.

Evaluate

= qjqZz1N+poo=