Chapter 1. Calculus Tutorial 2.3.022

1.1 Problem Statement

eval rand(2,3);

eval rand(12,19);

eval rand(1,3)

eval (2*$cp)+1;

eval (-1*$c);

eval pow(($b-$c*pow($a,2)),4);

eval pow($a,8);

eval round($answN/$answD,2);

Evaluate the limit using the Basic Limit Laws and limits and

1.2 Step 1

Recall that the Power Law states that for any positive integer n,

Question Sequence

Question 1.1

Apply the Power Law to the given problem.

z = h4XZagboIgc=

2

Correct.

Try again.

Incorrect.

1.3 Step 2

Recall that the sum law states that if and exist, then exists and

Question Sequence

Question 1.2

Apply the sum law to

z = ebcB+oSkYrE=

2

Correct.

That's not right. Check your work.

Incorrect.

Question 1.3

The second limit in the sum can be evaluated using , but to evaluate

we need to simply it further.

To rewrite as , we use the p8IK/qhNKAEnLJaAmUwnPTvA9HRwKuqWibQXN0IleoDE7J0B/CkSXFMCesU7E0dXDiBGu3LWt2T3rlRk.

Correct.

That's not right. Check your work.

Incorrect.

1.4 Step 3

Recall that the Product Law states that if and exist, then

.

We can apply the Product Law to since it can be expressed as .

Question 1.4

Apply the Product Law to

z = HvPwyjo89ro=

2

Correct.

That's not right. Check your work.

Incorrect.

Note: we could have also used the Power Rule to find this limit.

1.5 Step 4

Evaluate the limit using the Basic Laws and the limits and .

Question 1.5

where w=nc1ItEz0kR4= and z=ebcB+oSkYrE=.

Thus the value of the limit (rounded to two decimal places) is qjqZz1N+poo=.

2

Correct.

When applying the Limit Laws, in the last step, make the appropriate substitutions and evaluate.

Incorrect.