2011_Tutorial_1 - NATIONAL UNIVERSITY OF SINGAPORE...

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Unformatted text preview: NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA 1505 Mathematics I Tutorial 1 1. Let f ( x ) = 6 x and g ( x ) = p | 3- x | . Find an expression for ( g ◦ f )( x )- ( f ◦ g )( x ). Ans. q | 3- 6 x | - 6 √ | 3- x | . 2. Find the first derivatives of the following functions. (a) y = ax + b cx + d (b) y = sin n x cos( mx ) (c) y = e x 2 + x 3 (d) y = x 3- 4( x 2 + e 2 + ln2) (e) y = sin θ cos θ- 1 ¶ 2 (f) y = t tan(2 √ t ) + 7 (g) r = sin( θ + √ θ + 1) (h) s = 4 cos x + 1 tan x Ans. (a) y = ad- bc ( cx + d ) 2 (b) y = n sin n- 1 x cos x cos mx- m sin n x sin mx (c) y = e x 2 + x 3 (2 x + 3 x 2 ) (d) y = 3 x 2- 8 x (e) y =- 2sin θ (cos θ- 1)- 2 (f) y = √ t sec 2 (2 √ t ) + tan(2 √ t ) (g) r = 2 √ θ +1+1 2 √ θ +1 cos( θ + √ θ + 1) (h) s = 4tan x sec x- csc 2 x 3. Coffee is drained from a conical filter into a cylindrical coffeepot at the rate of 10 in 3 /min....
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This note was uploaded on 01/05/2012 for the course MATHEMATIC MA1505 taught by Professor Freudleong during the Spring '10 term at National University of Singapore.

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2011_Tutorial_1 - NATIONAL UNIVERSITY OF SINGAPORE...

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