Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #41 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given   and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

Example Question #42 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given   and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

 

Example Question #43 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given   and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

 

 

 

Example Question #44 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

Example Question #41 : Parametric Form

Find   when  and .

Possible Answers:

Correct answer:

Explanation:

If  and , then we can use the chain rule to define  as 

.  

We use the power rules

  and where  is a constant, the constant rule

 where   is a constant, and the additive property of derviatives 

.

In this case

 

 and

 ,

therefore 

Example Question #46 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

Example Question #51 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

Example Question #52 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the answers provided

Correct answer:

Explanation:

Given  and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

 

 

Example Question #53 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given  and ,  let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

 

 

Example Question #54 : Parametric Form

Given  and , what is  in terms of  (rectangular form)?

Possible Answers:

None of the above

Correct answer:

Explanation:

Given   and , let's solve both equations for :

Since both equations equal , let's set them equal to each other and solve for :

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