Calculus 1 Assignment 1

Assignment 3 (Chapter 2: Differentiation)

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Assignment 3 (Chapter 2: Differentiation) Due date: Wednesday 21st May 2008 Q1. Find an equation for the line perpendicular to the tangent to the curve y = x 2 − 2 x + 1 at the point (0,1). Q2. Given y = ln u and u = (tan 2 x + ln 2 x) 2 , find dy . dx

Q3. Find f ′(x ) : 1) f ( x ) = e ( x + ln x ) 2) f ( x ) = 4 2 + sin( 2 x) 2

⎛

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⎞ ⎟⎟ ⎝ 2x + 1 ⎠ 4) f ( x ) = cos[ln(sin x 4 )]

3) f ( x ) = tan ⎜⎜

x

Q4. Use implicit differentiation to find y ′ : 1) x ( x + y ) 2 = x 2 + y 2 2) x + sec(xy ) = π 3) e x y − ln y = x 2

Q5. Find the tangent line to the curve 2 xy + π cos y = π at the point (1, π / 2) .