Page 28 - Engineering Mathematics Workbook_Final

Calculus

(x  ) 2 e 4 e 2
−
(a) 1+ + ..... (c) (d)
3! 4! 2!

(x − ) 2 x 2 y 2 z 2
(b) 1− + + .....
3! 119. If u = x y z then
1 1 1
−
(x  ) 2
(c) 1− + ..... u + u + u =
3! x y z

(a) 0 (b) 1
−
(x  ) 2
(d) 1− + .....
−
+
+
3! (c) x y z (d) ( 2 x + y + ) z
)
+
117. The Taylor series expansion of 120. If u = f ( , r s where r = x y ,
 1 x 
+
−
log       at x = 0 is s = x y then u + x u = y
−
 1 x 
(a) 2u (b) 2u
 x 3 x 5  r s




(a) 2 x + + + .... − −


 3 5  (c) 2u (d) 2u
s
r
)
−
=
 x 3 x 5  121. If z = f ( , x y where x e + u e ,
v


(b) 2 x − + + ... − u v




 3 5  y = e − e then z − u z = v
 x 2 x 4  (a) xz − yz (b) xz + yz

(c) 2    + + .... x y x y


 2 4  (c) xz + yz (d) xz − yz
y x y x
4
 x 2 x 4    x + y 4  

(d) 2    − + .... 122. If u = log   x + y   then


 2 4   
 2 u +  2 u + 2  2 u
2
x
118. In the taylor series expansion of e , x  x 2 2xy   y  y 2 =
x y
4
about x = 2, the coefficient of ( x − ) 2
(a) 0 (b) 3
is
(c) -3 (d) 1/3
1 e 2
(a) (b)
4! 4!

26