RogaCalcET2 2.5.013.Tutorial.SA.

Problem Statement

eval rand(5,9);

9+1;

10*9-9;

9*9;

2*81;

eval 10*9+9;

eval 2*(9+9);

eval round(99/36,2);

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

Step 1

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

Question Sequence

Question 1

For the given rational function , evaluate the limit of the numerator and denominator as x approaches 9.

Incorrect.

Correct.

Step 2

Question Sequence

Since the rational function has an indeterminate form of the type at x = 9, 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 3

where z = .

Correct.

Incorrect.

Step 3

Since the limit is being evaluated as x approaches 9 (meaning for all values of x near 9, but not equal to 9), we can try to evaluate by applying the Quotient Law for evaluating limits.