{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

samplequiz1

# samplequiz1 - SOLUTIONS TO QUIZ 1 Question 1[6marks Let f x...

This preview shows pages 1–2. 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: SOLUTIONS TO QUIZ 1 Question 1 [6marks] Let f ( x ) be the function defined by f ( x ) = q 1 + 1 /x , x > 0. 1(a) Find the derivative f ( x ) using only first principles. 1(b) Find an equation of the tangent line to the graph of y = f ( x ) at x = 1 / 3 . Solution to Question 1: 1(a) f ( x ) = lim h → f ( x + h )- f ( x ) h = lim h → q 1 + 1 / ( x + h )- q 1 + 1 /x h = lim h → 1 + 1 / ( x + h )- (1 + 1 /x ) h ( q 1 + 1 / ( x + h ) + q 1 + 1 /x ) = lim h →- 1 x ( x + h )( q 1 + 1 / ( x + h ) + q 1 + 1 /x ) =- 1 2 x 2 q 1 + 1 /x . 1(b) By a simple computation f (1 / 3) = 2 and f (1 / 3) =- 9 / 4, and therefore the tangent line is given by y- 2 =- 9 / 4( x- 1 / 3). Question 2 [6 marks] Compute the following limits. 2(a) lim x →∞ ( √ x 2 + ax- √ x 2- ax ), where a is a constant. 2(b) lim x → 1 ( x 2- 1) / ( √ x + 8- 3). 2(c) lim x → (2 x + 3 x 2 ) / (3 x- 2 x 2 ). Solution to Question 2: 2(a) lim x →∞ ( √ x 2 + ax- √ x 2- ax ) = lim x →∞ x 2 + ax- ( x 2- ax...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

samplequiz1 - SOLUTIONS TO QUIZ 1 Question 1[6marks Let f x...

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

View Full Document
Ask a homework question - tutors are online