Short Questions (Question 26 & 27)


Question 26 (3 marks):
Find the value of
( a )  lim x1 ( 7 x 2 ), ( b ) f''( 2 ) if f'( x )=2 x 3 4x+3.

Solution:
(a)
lim x1 ( 7 x 2 ) =7 ( 1 ) 2 =6

(b)
 f'( x )=2 x 3 4x+3 f''( x )=6 x 2 4 f''( 2 )=6 ( 2 ) 2 4   =244   =20



Question 27 (4 marks):
It is given that L = 4t t2 and x = 3 + 6t.
(a) Express dL dx in terms of t.
(b) Find the small change in x, when L changes from 3 to 3.4 at the instant t = 1.

Solution:
(a)
Given L=4t t 2  and x=3+6t L=4t t 2 dL dt =42t x=3+6t dx dt =6 dL dx = dL dt × dt dx dL dx =( 42t )× 1 6 = 42t 6 = 2t 3


(b)
δL=3.43=0.4 δL δx dL dx δx=δL÷ δL δx δx=δL× δx δL =0.4× 3 2t = 2 5 × 3 2t = 6 5( 2t ) When t=1,  δx= 6 5( 21 ) = 6 5