# ws17 - WORKSHEET 17 Fall 1995 1 Find y both implicitly and...

This preview shows pages 1–2. Sign up to view the full content.

WORKSHEET 17 - Fall 1995 1. Find y 0 both implicitly and explicitly for each relation below. a) x 1 / 2 + y 1 / 2 =1 b) | x | + | y | =1 c) x 2 + y 2 =1 d) x 3 + y 3 =1 2. Find y 0 for each of the parts of problem 1. 3. Consider the curve x 2 + y 2 - xy +3 x - 9=0. a) Find dy dx . b) Find two points on the curve where the tangent is parllel to the y -axis. 4. Let F ( u, v ) be a function of the two quantities u and v . Suppose also that u and v depend on another variable x . Then ultimately, F may be thought of as a function of x . Speci±cally, we may de±ne a function ˜ F ( x )by ˜ F ( x )= F ( u ( x ) ,v ( x )) . A generalized version of the chain rule applies here: d ˜ F dx = ∂F ∂u du dx + ∂F ∂v dv dx . Now suppose that we have de±ned y implicitly as a function of x by some equation F ( x, y )=0 . Use the above di²erentiatition rule to show that dy dx = - ∂F/∂x ∂F/∂y . (Hint: If

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.

### Page1 / 2

ws17 - WORKSHEET 17 Fall 1995 1 Find y both implicitly and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online