Numerical Analysis Homework: Finding Roots of Nonlinear Equations, Exercises of Stochastic Processes

The third homework assignment for a numerical analysis course. Students are required to find the roots of given nonlinear equations using three different methods: bisection, newton-raphson, and secant. For each method, they need to plot the function's graph and choose an appropriate initial guess to find the root value correct to the specified decimal places.

Typology: Exercises

2011/2012

Uploaded on 08/12/2012

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COURSE: NUMERICAL ANALYSIS
Home Work # 2
Due Date: One week from date of receiving the Home work.
Question No.1
Find at least one root of the following nonlinear equation by bisection method. First plot
a graph of function and then select a suitable initial guess. Find root value correct to 3
decimal places.
(a) 295 23 = xx
(b) xx= 10)exp(
Question No.2
Find at least one root of the following nonlinear equation by Newton - Raphson method.
First plot a graph of function and then select a suitable initial guess. Find root value
correct to 4 decimal places.
(a)
295 23 = xx
(b)
xx = 10)exp(
(c)
010.tan = xx
Question No.3
Find at least one root of the following nonlinear equation by secant method. First plot a
graph of function and then select a suitable initial guess. Find root value correct to 4
decimal places.
(a) 295 23 = xx
(c) exp(x) = (x + 1)/(x - 1)
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COURSE: NUMERICAL ANALYSIS

Home Work # 2

Due Date: One week from date of receiving the Home work.

Question No. Find at least one root of the following nonlinear equation by bisection method. First plot a graph of function and then select a suitable initial guess. Find root value correct to 3 decimal places.

(a) x^3 − 5 x^2 = 29 (b) exp( x ) = 10 −x

Question No. Find at least one root of the following nonlinear equation by Newton - Raphson method. First plot a graph of function and then select a suitable initial guess. Find root value correct to 4 decimal places.

(a) x^3 − 5 x^2 = 29 (b) exp( x ) = 10 −x

(c) tan x− x= 0. 01

Question No. Find at least one root of the following nonlinear equation by secant method. First plot a graph of function and then select a suitable initial guess. Find root value correct to 4 decimal places.

(a) x^3 − 5 x^2 = 29 (c) exp(x) = (x + 1)/(x - 1)

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