### All Calculus 1 Resources

## Example Questions

### Example Question #1721 : Functions

Take the limit

**Possible Answers:**

**Correct answer:**

First, multiply the numerator and denominator by and it turns into

Factor the numerator and then cancel out the 'x+2'

After taking the limit, the answer is

### Example Question #1 : How To Find The Meaning Of Functions

If this limit is true, then what is the value of 'a'?

**Possible Answers:**

**Correct answer:**

Factor the numerator

Cancel the , plug in the limit and then solve for 'a'

### Example Question #1721 : Functions

We have a line described as . Find the minimum distance between the origin and a point on that line.

**Possible Answers:**

**Correct answer:**

We have the origin and a point located on the line. That point represents the minimum distance to the orgin. Apply the distance formula to these two points,

Plug in the line equation, take the derivative, set it equal to zero, and solve for x.

Use this value to find

So we have the point , which is closest to the origin. We can now find its distance from that origin.

### Example Question #4 : Meaning Of Functions

We have the following,

What is c?

**Possible Answers:**

**Correct answer:**

First, factor the numerator of the integrand.

Cancel out

Perform the integral and then solve for

### Example Question #5 : Meaning Of Functions

If , find

**Possible Answers:**

**Correct answer:**

Taking the derivative of an integral yields the original function, but because we have a different variable in the integration limits, the variable switches

### Example Question #6 : Meaning Of Functions

Evaluate

**Possible Answers:**

**Correct answer:**

using integration identities:

### Example Question #7 : Meaning Of Functions

Evaluate

**Possible Answers:**

**Correct answer:**

evaluate at

### Example Question #2 : How To Find The Meaning Of Functions

Evaluate

**Possible Answers:**

**Correct answer:**

Intergation by substitution

new endpoints:

New Equation:

at

### Example Question #3 : How To Find The Meaning Of Functions

What is ?

**Possible Answers:**

undefined

1

0

-1

**Correct answer:**

0

The relationship between and x is an exponential relationship; is going to exponentially faster than is going to . One way to prove this is to write and use L'Hôpital's rule:

### Example Question #1 : How To Find The Meaning Of Functions

Where is discontinuous? Are those discontinuities removable?

**Possible Answers:**

Essential discontinuities at and .

Removable discontinuities at and .

Removable discontinuities at and .

Removable discontinuity at , essential discontinuity at .

Removable discontinuity at , essential discontinuity at .

**Correct answer:**

Removable discontinuity at , essential discontinuity at .

The rational function has a denominator with two roots, and . These are discontinuities.

Factoring both top and bottom and canceling a term tells us that this function is equal to

except at . This point is a removable discontinuity. is therefore an essential discontinuity where the ratio goes to .