Calculus Tutorial 2.3.022

Problem Statement

eval rand(2,3);

eval rand(12,19);

eval rand(1,3)

eval (2*1)+1;

eval (-1*3);

eval pow((15-3*pow(3,2)),4);

eval pow(3,8);

eval round(20736/6561,2);

Evaluate the limit using the Basic Limit Laws and limits and

Step 1

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

Question Sequence

Question 1

Apply the Power Law to the given problem.

z =

2

Correct.

Try again.

Incorrect.

Step 2

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

Question Sequence

Question 2

Apply the sum law to

z =

2

Correct.

That's not right. Check your work.

Incorrect.

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 4

Apply the Product Law to

z =

2

Correct.

That's not right. Check your work.

Incorrect.

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

Step 4

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

Question 5

where w= and z=.

Thus the value of the limit (rounded to two decimal places) is .

2

Correct.

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

Incorrect.