Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

  
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,434 questions

17,804 answers

1,438 comments

69,625 users

Find an equation of the tangent to the curve at the given point by two methods:

0 votes

 Find an equation of the tangent to the curve at the given point by two methods: (a) without eliminating the parameter and (b) by first eliminating the parameter.

asked Feb 2, 2015 in CALCULUS by anonymous

2 Answers

0 votes

Step 1 :  

(a)

The parametric equations are , and the point is .

Substitute the point in .

The slope of the tangent line is at .

Consider .

Apply derivative on each side with respect to t.

Consider .

Apply derivative on each side with respect to t.

  

Step 2 :

Chain rule of derivatives :

Substitute and image in above expression.

Substitute in above equation.

The slope is .

The point-slope form of a line equation is .

Substitute and the point in above equation.

The tangent line equation is   

Solution :

The tangent line equation is

answered Feb 2, 2015 by Thomas Apprentice
0 votes

Step 1 :  

(b)

The parametric equations are , and the point is .

The slope of the tangent line is the derivative of the function at .

Consider .

Rewrite the expression :

Substitute in .

Apply derivative on each side with respect to x.

Substitute in above equation.

The slope is .

Step 2 :

The point-slope form of a line equation is .

Substitute and the point in above equation.

The tangent line equation is

Solution :  

The tangent line equation is

answered Feb 2, 2015 by Thomas Apprentice

Related questions

...