# To guess: The value of lim x → − 3 x 2 − 3 x x 2 − 9 .

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 2.2, Problem 18E
To determine

## To guess: The value of limx→−3x2−3xx2−9.

Expert Solution

The limit of the given function does not exist.

### Explanation of Solution

Given:

The values of x are 2.5,2.9,2.95,2.99,2.999,2.9999,3.5,3.1,3.05,3.01,

3.001 and 3.0001.

Calculation:

Since x approaches −3, the values 3.5,3.1,3.05,3.01,3.001 and 3.0001 are to the left of −3 and the values 2.5,2.9,2.95,2.99,2.999, and2.9999 are to the right of −3.

Evaluate the function (correct to 6 decimal places) when x=3.5,3.1,3.05,3.01,3.001 and 3.0001 as shown in the below table.

 x x2−3x x2−9 f(x)=x2−3xx2−9 −3.5 22.75 3.25 7 −3.1 18.91 0.61 31 −3.05 18.4525 0.3025 61 −3.01 18.0901 0.0601 301 −3.001 18.009 0.006001 3,001 −3.0001 18.0009 0.0006 30,001

Here, the value of f(x) approaches the large negative value as x closer to −3 from the left side.

That is, limx3x23xx29=.

Evaluate the function (correct to 6 decimal places) when x=2.5,2.9,2.95,2.99,2.999, and2.9999 as shown in the below table.

 x x2−3x x2−9 f(x)=x2−3xx2−9 −2.5 13.75 −2.75 −5 −2.9 17.11 −0.59 −29 −2.95 17.5525 −0.2975 −59 −2.99 17.9101 −0.0599 −299 −2.999 17.991 −0.006 −2,999 −2.9999 17.9991 −0.0006 −29,999

Here, the value of f(x) gets closer to the largest positive value as x approaches to 0 from the right side.

That is, limx3+x23xx29=.

Since the left-hand limit and the right-hand limit are not the same, the limit of the function does not exist.

Thus, it can be guessed that limx3x23xx29 does not exist.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!