Page 180 - ADVANCED MATH F.5

Form Five Form Five

(b) z ∂ = (2x + ) y e x + 2 xy ; z ∂ = xe x + 2 xy
x ∂ y ∂

z ∂ z ∂
FOR ONLINE READING ONLY
(c) = 3x + 2 2 ; y = 2x + 4y 3
x ∂ y ∂
z ∂ 3x 2 y 3 z ∂ 2x 3 3y 2
(d) = + ; = − −
x ∂ y 2 x 2 y ∂ y 3 x

(e) z ∂ = 4x − 6 ; y z ∂ = − 6x + 2y
x ∂ y ∂
z ∂ z ∂
(f) = 2cos (2x + 3y ); = 3cos (2x + 3y )
x ∂ y ∂

30. 1.85 cm

100π 400
31. Length l = 4 π + cm and l = 4 π + cm
2
1

32. − 3 m / min 33. − 86 m/sec
π

Velocity
34. Velocity (v) ( 4t= − + 10 ) m/sec, acceleration (a) = – 4 m/s
2
35. (a) z ∂ = 16 (b) ∂ 2 z = − 8
xy
x ∂ ∂∂

63  63  2
37. r = 3 cm; h =  3  cm
π  π 
 

)
1,
38. ( 1,2− ) maximum; ( ) 2 minimum and (0,0 point of

inflexion
dy 2
2
39. 0.16% 40. = −
dx 2 3

174
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:46
ADVANCED MATH F.5 TG CHAPTERS.indd 174
ADVANCED MATH F.5 TG CHAPTERS.indd 174 30/06/2024 18:02:46