Numerical Methods Practice Questions and Answers

ENGINEERING MATHEMATICS



NUMERICAL METHODS




QUESTIONS AND ANSWERS



ZFS Co.

, *


1 .
(a) (P-P 1 =
10


1- = 10


= 110


pY e'(1 4)
-


= + 10




:
[-2 .
718010 ,
2 . 718554]#



(b) p
* = >(1 = 10
-




4)

:
(1 .
912740 ,
1 .
913122]#




(5 +(i) i
794
+ -
=
2 .
627



=
1 .
2663



~ 1 26.




1p-p /
*
Absolute error =




794
26 /
1627 1
-

= .




= 0 .
63477x10-2#

,3 .
-
10n + be
-

3 = -
15 15
.




X
p p
-




Relative error =
P
-
10n + be -
13/62) + 15 . S
I
-
10n + be -
13/62)



= 0 . 30503x10-3#




4
. (a) f(u0) = sin no



=
sin I




J(x0) = f(x0 + 2)


=
sin (no + 2)



6)
-
=
sin (1 + (5x 10




( + (x0) -

T(x0)) =
(sin 1 -
sin(1 + 25x10
-




8)))
-
S
0
27015x10#
=
.




Absolute error = 1f (no) x El

= 120s 1((5x103(1

= 0 . 270151x10#

, (b) +(40) = cos no



=
cos I




J(x0) = f(x0 + 2)


=
cos(no + E)



6)
-
=
cos(1 + (S x 10



%)
-


cos 1 -
cos (1 + 15 x 10

1 + (20) -

E(x0))/(f(x0)) = cos




= 0 .
77870511 x 103




17 2)xG/
220 +
Relative error =
f(x0)


6))
3))(3
(
- -
-
Sinc + (5x10 x 10
=

COS


= 0 . 778706x10#




⑱
1 - COS 11

.
S f(x) = x2

1-11-2 sink(n/2)
I
22
?
2 sin (n/2)
=
22


= 2
(sin(12)
= h(x)



sin

g(x) = 22(1 + cosa)

#
+ cos n)(1 -
cosn)
=

22(1
20s 2) +


I -
cos 2

=
22


= f(x)




:
f(u) =
g(x) = h(n) shown #
,