Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

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Example Questions

Example Question #65 : Parametric Form

Convert the following parametric equation to rectangular form:

Possible Answers:

Correct answer:

Explanation:

To convert from parametric to rectangular coordinates, we must eliminate the parameter by finding t in terms of x or y:

We will start by taking the exponential of both sides of the equation . Recall that .

Therefore we get,  

.

Now, replace t with the above term in the equation for x:

 

Example Question #66 : Parametric Form

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

Possible Answers:

Correct answer:

Explanation:

Given  and , wet's solve both equations for :

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

Example Question #67 : Parametric Form

Given  and , what is  in terms of 

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 #68 : Parametric Form

Given  and , what is  in terms of 

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 #69 : Parametric Form

Given  and , what is  in terms of 

Possible Answers:

None of the above

Correct answer:

Explanation:

Given   and , wlet's solve both equations for :

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

Example Question #70 : Parametric Form

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

Possible Answers:

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 #71 : 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 #72 : 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 #73 : 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 #74 : Parametric Form

Find dy/dx at the point corresponding to the given value of the parameter without eliminating the parameter:

Possible Answers:

Correct answer:

Explanation:

The formula for dy/dx for parametric equations is given as:

From the problem statement:

If we plug in t=3, into the above equations:

This is one of the answer choices.

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