Chapter 1. Calculus Tutorial 2.7.008

1.1 Problem Statement

{5,6,7,8,9}

{2,3,4,5,6,7,8,9}

eval round($a/$c,2)

Evaluate the limit

1.2 Step 1

In general, we wish to use the Quotient Law to evaluate limits of rational functions. Recall the Quotient Law.

If and exist (as a finite number) and then we have the following equation.

To see if we can directly apply the Quotient Law to evaluate , use Basic Limit Laws to determine the limit as x approaches ∞ of both the numerator and denominator.

Recall that for all n > 0.

Question Sequence

Question 1.1

3LecBr2w/JA=

(Enter "inf" for ∞ and "-inf" for -∞)

Incorrect.

Correct

Question 1.2

Since both of these limits sGe9BG4ptbLdvBlRE8fTlQ== exist as finite numbers, we 98RZuska2DoKNkUANZwGUQ== directly apply the Quotient Law.

Incorrect.

Correct.

1.3 Step 2

Question 1.3

Since we cannot apply the Quotient Law directly, we will divide both the numerator and the denominator by the highest power of x present in the denominator to find an equivalent rational fraction. Therefore, we will divide both the numerator and denominator by x². We can do this because we are considering the limit as x approaches ∞, and so we need not worry about dividing by zero.

where a=XvVM00l89Is=.

where b=UYinCekNO0E= and c=FmAhxBkQqN0=.

Incorrect.

Correct.

1.4 Step 3

We will now be able to apply the Quotient Law and other Basic Limit Laws to the new limit from step 2 since the limits in the numerator and denominator will be finite.

In evaluating the new limit, we will also have to use the fact that for any whole number n, we have