{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 2011_Tutorial_1 - NATIONAL UNIVERSITY OF SINGAPORE...

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

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 + ln 2) (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 0 = ad - bc ( cx + d ) 2 (b) y 0 = n sin n - 1 x cos x cos mx - m sin n x sin mx (c) y 0 = e x 2 + x 3 (2 x + 3 x 2 ) (d) y 0 = 3 x 2 - 8 x (e) y 0 = - 2 sin θ (cos θ - 1) - 2 (f) y 0 = t sec 2 (2 t ) + tan(2 t ) (g) r 0 = 2 θ +1+1 2 θ +1 cos( θ + θ + 1) (h) s 0 = 4 tan 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. (a) How fast is the level in the pot rising when the coffee in the cone is 5 in. deep? (b) How fast is the level in the cone falling then? (Volume of cone: 1 3 × base area × height) Ans. (a) 10 9 π in/min; (b) 8 5 π in/min.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
MA1505 Tutorial 1 4. For the following functions, find y 0 and y 00 . (a) x 2 / 3 + y 2 / 3 = a 2 / 3 , 0 < x < a , 0 < y (b) y = (sin x ) sin x , 0 < x < π 2 (c) x = a cos t , y = a sin t Ans. (a) y 0 = - r ( a x ) 2 / 3 - 1, y 00 = a 2 / 3 3 x 4 / 3 p a 2 / 3 - x 2 / 3 . (b) y 0 = (sin x ) sin x (1 + ln sin x ) cos x , y 00 = (sin x ) sin x [(1 + ln sin x ) 2 cos 2 x
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

2011_Tutorial_1 - NATIONAL UNIVERSITY OF SINGAPORE...

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

View Full Document
Ask a homework question - tutors are online