Chemical Engineering
Numerical Methods - Optimization
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Aim
Theory
Pretest
Procedure
Simulation
Posttest
References
Contributors
Feedback
Newton Raphson Method
Choose difficulty:
Beginner
Intermediate
Advanced
Initial guess
x
1
=
1
\text{Initial guess} \quad x1 = 1
Initial guess
x
1
=
1
x
2
=
x
1
−
f
(
x
1
)
d
f
(
x
1
)
x2 = x1 - \frac{f(x1)}{df(x1)}
x
2
=
x
1
−
df
(
x
1
)
f
(
x
1
)
equation
=
x
2
−
c
o
s
(
x
)
\text{equation } = x^2-cos(x)
equation
=
x
2
−
cos
(
x
)
d
f
(
x
)
=
2
x
+
s
i
n
(
x
)
df(x) = 2x + sin(x)
df
(
x
)
=
2
x
+
s
in
(
x
)
What is function value of 3rd iteration using Newton Raphson method?
\text{What is function value of 3rd iteration using Newton Raphson method?}
What is function value of 3rd iteration using Newton Raphson method?
a: 0.03382
Explanation
Explanation
b: 0.00026
Explanation
Explanation
c: 0
Explanation
Explanation
d: 0.00018
Explanation
Explanation
Initial guess
x
1
=
1
\text{Initial guess} \quad x1 = 1
Initial guess
x
1
=
1
x
2
=
x
1
−
f
(
x
1
)
d
f
(
x
1
)
x2 = x1 - \frac{f(x1)}{df(x1)}
x
2
=
x
1
−
df
(
x
1
)
f
(
x
1
)
equation
=
x
2
−
c
o
s
(
x
)
\text{equation } = x^2-cos(x)
equation
=
x
2
−
cos
(
x
)
d
f
(
x
)
=
2
x
+
s
i
n
(
x
)
df(x) = 2x + sin(x)
df
(
x
)
=
2
x
+
s
in
(
x
)
What is root value of 3rd iteration using Newton Raphson method?
\text{What is root value of 3rd iteration using Newton Raphson method?}
What is root value of 3rd iteration using Newton Raphson method?
a: 0.82413
Explanation
Explanation
b: 0.83822
Explanation
Explanation
c: 0.82413
Explanation
Explanation
d: 0.82413
Explanation
Explanation
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