### All Calculus 1 Resources

## Example Questions

### Example Question #2783 : Calculus

Evaluate:

**Possible Answers:**

The limit does not exist.

**Correct answer:**

In order to evaluate the limit, lets factor the numerator.

Now we can simplify this expression to

.

Now we plug in 10.

### Example Question #2784 : Calculus

Evaluate:

**Possible Answers:**

The limit does not exist.

**Correct answer:**

If we plug in , we get

Since we get , we can use L'Hopitals rule.

L'Hopitals rule is if we have one of the following cases

where a is any real number, then

After applying L'Hopitals rule, we get

Now if we plug in , we get

### Example Question #2785 : Calculus

Let represent the growth rate of the city of Tucson at a year where represents the year . Give a practical interpretation of .

**Possible Answers:**

The average rate of change of people between and .

The total increase in people in Tucson from to .

The number of cats in people in .

The average number of people between and .

The rate of change in the number of people in .

**Correct answer:**

The total increase in people in Tucson from to .

The integral of the rate of change of people gives the change in the number of people over the time interval. However, it does not tell you how many people are present because it contains no information on how many people were present initially. (Think that if you integrate you get *. *Here * *denotes the number of people added and denotes the initial number of people.)

### Example Question #2786 : Calculus

Find the critical point(s) of .

**Possible Answers:**

and

and

and

**Correct answer:**

To find the critical point(s) of a function , take its derivative , set it equal to , and solve for .

Given , use the power rule

to find the derivative. Thus the derivative becomes, .

Since :

The critical point is .

### Example Question #2787 : Calculus

Find the critical point(s) of .

**Possible Answers:**

and

and

and

**Correct answer:**

To find the critical point(s) of a function , take its derivative , set it equal to , and solve for .

Given , use the power rule to find the derivative.

Thus the derivative becomes, .

Since :

The critical point is .

### Example Question #31 : Meaning Of Functions

Which of the following is not a function?

**Possible Answers:**

**Correct answer:**

A function is defined when each value of x yields a single value of y (ordered pairs). The expression

is not a function because there are two values of f(x) for which a single value of x (7) creates. f(7) can be either 3(7)+2=19 or 3(7)-2=21, and is therfore not a function.

### Example Question #2789 : Calculus

Evaluate:

**Possible Answers:**

The limit does not exist

**Correct answer:**

To evaluate the limit, we can factor the numerator

Now we simplify and evaluate.

### Example Question #2790 : Calculus

Evaluate:

**Possible Answers:**

**Correct answer:**

In order to evaluate the limit, we need to factor the numerator

Now we can simplify the expression to

.

Now we can plug in 1 to get

.

### Example Question #31 : How To Find The Meaning Of Functions

Evaluate the limit:

**Possible Answers:**

None of the other answers

**Correct answer:**

By applying L'Hôpital's rule, we can find the limit by evaluating

The function is now written as

Plugging in 0 gives us

### Example Question #32 : How To Find The Meaning Of Functions

Which of the following statements is true regarding the behavior of functions with respect to its derivatives?

**Possible Answers:**

The natural log is a decreasing function because its second derivative is always negative.

The second derivative tells you when the function changes from decreasing to increasing and vice versa.

If at a point, the derivative is positive and the second derivative in negative, the function is decreasing at an increasing rate.

An example of a point of inflection is where the function goes from increasing at a decreasing rate to increasing at an increasing rate.

**Correct answer:**

An example of a point of inflection is where the function goes from increasing at a decreasing rate to increasing at an increasing rate.

The statement

"An example of a point of inflection is where the function goes from increasing at a decreasing rate to increasing at an increasing rate."

is true. Point of inflection is when the function changes from concave up to concave down and vice versa. In the example above, the function changes from concave down (slopes are decreasing) to concave up (slopes are increasing).

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