Applied Mathematics for Electrical Engineering (3130908)

Question-4c ( ii )-OR

BE | Semester-3 Winter-2019 | 26-11-2019

Q4) (c ( ii ))

Let,

f (x) = x - \cos x

\Rightarrow f (0) = 0 - \cos 0 = - 1

\Rightarrow f (1) = 1 - \cos 1 = 0.46

Therefore, root lies between

[0, 1]

c = \frac{a + b}{2} = \frac{0 + 1}{2} = 0.5

$a (< 0)$	$b (> 0)$	$c$	$x^{2}$
$0$	$1$	$0.5$	$< 0$
$0.5$	$1$	$0.75$	$> 0$
$0.5$	$0.75$	$0.63$	$< 0$
$0.63$	$0.75$	$0.69$	$< 0$
$0.69$	$0.75$	$0.72$	$< 0$
$0.72$	$0.75$	$0.74$	$< 0$
$0.74$	$0.75$	$0.75$	$> 0$
$0.74$	$0.75$	$0.75$	$-$

x = 0.75

is the required root.