{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# sols3 - SOLUTIONS TO HOMEWORK ASSIGNMENT#3 1 Each of the...

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

SOLUTIONS TO HOMEWORK ASSIGNMENT #3 1. Each of the following questions can be done with little computation. Suppose f ( x ), g ( x ) are functions satisfying f ( a ) = α, g ( a ) = β, f 0 ( a ) = γ and g 0 ( a ) = δ for some a, α, β, γ, δ. (a) Compute the derivative of f ( x ) + g ( x ) at x = a . (b) Compute the derivative of f ( x ) g ( x ) at x = a . (c) Compute the derivative of f ( x ) /g ( x ) at x = a . (d) Compute the derivative of x 2 f ( x ) - x 3 g ( x ) at x = a . Solutions: (a) d dx ( f ( x ) + g ( x )) x = a = ( f 0 ( x ) + g 0 ( x )) x = a = f 0 ( a ) + g 0 ( a ) = γ + δ. (b) d dx ( f ( x ) g ( x )) x = a = ( f 0 ( x ) g ( x ) + f ( x ) g 0 ( x )) x = a = f 0 ( a ) g ( a ) + f ( a ) g 0 ( a ) = γβ + αδ (c) d dx f ( x ) g ( x ) x = a = g ( x ) f 0 ( x ) - f ( x ) g 0 ( x ) ( g ( x )) 2 x = a = βγ - αδ β 2 (d) d dx ( x 2 f ( x ) - x 3 g ( x ) ) x = a = ( 2 xf ( x ) + x 2 f 0 ( x ) - 3 x 2 g ( x ) - x 3 g 0 ( x ) ) x = a = 2 + a 2 γ - 3 a 2 β - a 3 δ 2. Each of the following questions can be done with little computation. Suppose f ( x ), g ( x ) are functions satisfying f (2) = 4 , g (2) = 4 , f 0 (2) = - 1 and g 0 (2) = 1. (a) Compute the derivative of f ( xg ( x ) - 6) at x = 2. (b) Compute the derivative of f ( x ) / p g ( x ) at x = 2. Solutions: (a) d dx ( f ( xg ( x ) - 6)) x =2 = f 0 ( ( xg ( x ) - 6) x =2 ) × ( ( g ( x ) + xg 0 ( x )) x =2 ) = f 0 (2) × 6 = - 6 (b) d dx f ( x ) p g ( x ) !

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.

{[ snackBarMessage ]}

### Page1 / 3

sols3 - SOLUTIONS TO HOMEWORK ASSIGNMENT#3 1 Each of the...

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

View Full Document
Ask a homework question - tutors are online