Assignment 2
1. If u  log  x 4  y 4  /  x  y   , show that
 x  2 y  3z 
2. If u  sin 1 
 , show that
 x8  y8  z 8 
x
x
u
u
y
3
x
y
u
u
u
 y  z  3tan u  0
x
y
z
u
u
 y
 5u
3. If u  x3 y 2 sin 1   , show that x  y
x
y
x
x2
and
2
 2u
 2u
2  u

2
xy

y
 20u
x 2
xy
y 2
x
u
u
 y
u
4. If u  xe x / y sin    ye y / x cos   , show that x  y
x
y
x
 y
5. Expand tan 1
y
in the neighbourhood of (1, 1) up to and inclusive of second degree
x
term.
6. Expand e x tan 1 y in powers of  x  1 and  y  1
7. Find the approximate value of 0.92.01 using Taylor’s Series.
8. Trace the curve y 2 ( x  1)  x3
9. Find the Inclined asymptote of the curve  x  y  ( x  2 y  2)  x  9 y  2 .
2
10. Trace the curve y 2 (a  x)  x2 (3a  x) .