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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
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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)