# Calculus 1 : Other Differential Functions

## Example Questions

### Example Question #31 : Other Differential Functions

Solve for  when

Explanation:

using the chain rule:

multiply the constant 9 into the second function to simplify answer

### Example Question #211 : Functions

Solve for  when

Explanation:

using the logarithm identities change the equation to base 10:

using lograthim identities simplify the numerator:

differentiate

Simplify

### Solve for  when

Explanation:

Using the product rule:

FOIL

Combine like-terms

### Example Question #32 : Other Differential Functions

Solve for  using implicit differentiation if

Explanation:

Differentiate the equation

Simplify

place all terms with  on one side and the other terms on the other side

Simplify

Divide and solve for

### Example Question #33 : Other Differential Functions

Solve for  using the Mean Value Theorem, rounded to the nearest hundredth place when

on the interval

Explanation:

Mean Value Theorem (MVT) =   on

### Example Question #34 : Other Differential Functions

Evaluate the limit:

Explanation:

Attempting to evaluate directly (plug in -1 for ) results in the indeterminate form:

Further analysis is required:

This final form can be evaluated directly:

### Example Question #31 : Other Differential Functions

Evaluate the limit:

Explanation:

Attempting to evaluate directly (plug in 2 for ) results in the indeterminate form:

Further analysis is required:

This final form can be evaluated directly:

### Example Question #35 : Other Differential Functions

Evaluate the limit:

Explanation:

We evaluate the limit directly (plug in 3 for ) and obtain:

from which we determine that the the function has a vertical asymptote at this point (it goes off to positive or negative infinity). The limit Does Not Exist.

### Example Question #36 : Other Differential Functions

Given:

Evaluate the limit:

Explanation:

This limit can be evaluated directly.

Recall that

So:

### Example Question #31 : Other Differential Functions

Given:

Evaluate the limit:

Explanation:

First observe that

Multiplying by  we obtain:

Limit of product is the product of limits:

From the Pre-Question Text:

So: