hw03-sol

# hw03-sol - Homework 3 Due 1 Find an equation of the tangent...

This preview shows pages 1–3. Sign up to view the full content.

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.

Unformatted text preview: Homework # 3 Due: 6/6/06 1. Find an equation of the tangent line to y = √ 2 x + 1 at the point (4,3). The equation of a tangent line to y = f ( x ) at ( a, b ) is ( y- b ) = f ( a )( x- a ). First, we write the equation as y = (2 x + 1) 1 2 d dx (2 x + 1) 1 2 = 1 2 (2 x + 1)- 1 2 (2 x ) = (2 x + 1)- 1 2 Evaluated at x = 4, we get (2(4) + 1)- 1 2 = 9- 1 2 = 1 3 . So the tangent line is y- 3 = 1 3 ( x- 4) 2. Draw a graph of a function f that has the properties g (0) = 0 g (0) = 3 g (1) = 0 g (2) = 1 3. Use the limit definition of the derivative to compute f ( a ) if f ( x ) = x 2 +1 x- 2 f ( a ) = lim h → f ( x + h )- f ( x ) h = lim h → ( x + h ) 2 +1 x + h- 2- x 2 +1 x- 2 h = lim h → ( x + h ) 2 +1 x + h- 2 ( x- 2 x- 2 )- x 2 +1 x- 2 ( x + h- 2 x + h- 2 ) h = lim h → (( x + h ) 2 + 1)( x- 2)- ( x 2 + 1)( x + h- 2) h ( x + h- 2)( x- 2) = lim h → ( x 2 + 2 xh + h 2 + 1)( x- 2)- ( x 2 + 1)( x + h- 2) h ( x + h- 2)( x- 2) = lim h → x 3 + 2 hx 2 + x 2 h 2 + x- 2 x 2- h ( x = lim...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

hw03-sol - Homework 3 Due 1 Find an equation of the tangent...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online