Calculus 1 : Other Differential Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #31 : Other Differential Functions

Solve for  when 

Possible Answers:

Correct answer:

Explanation:

using the chain rule:

 

multiply the constant 9 into the second function to simplify answer

Example Question #211 : Functions

Solve for  when 

Possible Answers:

Correct answer:

Explanation:

using the logarithm identities change the equation to base 10: 

using lograthim identities simplify the numerator:

differentiate

Simplify

Example Question #212 : Functions

Solve for  when

 

Possible Answers:

Correct answer:

Explanation:

Using the product rule: 

 

FOIL

Combine like-terms

Example Question #32 : Other Differential Functions

Solve for  using implicit differentiation if

 

Possible Answers:

Correct answer:

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

Possible Answers:

Correct answer:

Explanation:

Mean Value Theorem (MVT) =   on

Example Question #34 : Other Differential Functions

Evaluate the limit:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

Explanation:

This limit can be evaluated directly.

Recall that 

So: 

Example Question #31 : Other Differential Functions

Given:

 

Evaluate the limit:

Possible Answers:

Correct answer:

Explanation:

First observe that 

Multiplying by  we obtain:

Limit of product is the product of limits:

From the Pre-Question Text: 

So:

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