2011_Solution_1 - MA 1505 Mathematics I Tutorial 1...

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Unformatted text preview: MA 1505 Mathematics I Tutorial 1 Solutions 1. Note that ( g ◦ f )( x ) = q | 3- 6 x | and ( f ◦ g )( x ) = 6 √ | 3- x | . 2. (a) y = ax + b cx + d , y = a ( cx + d )- c ( ax + b ) ( cx + d ) 2 = ad- bc ( cx + d ) 2 (use quotient rule) (b) y = sin n x cos mx , y = n sin n- 1 x cos x cos mx- m sin n x sin mx (use product rule and chain rule) (c) y = e x 2 + x 3 y = e x 2 + x 3 (2 x + 3 x 2 ) (use chain rule) (d) y = x 3- 4( x 2 + e 2 + ln2), y = 3 x 2- 8 x (note that e 2 and ln2 are constants) Similarly, we find the derivatives in (e) - (h). (e)- 2sin θ (cos θ- 1)- 2 (use quotient and chain rule) (f) √ t sec 2 (2 √ t ) + tan(2 √ t ) (use product and chain rule) (g) 2 √ θ +1+1 2 √ θ +1 cos( θ + √ θ + 1) (use chain rule) (h) 4tan x sec x- csc 2 x (use quotient rule) 3. Let V c ( t ) be the volume of coffee in the cone at time t and V p ( t ) be the volume of coffee in the pot at time t ....
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2011_Solution_1 - MA 1505 Mathematics I Tutorial 1...

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