GATE CE 2026 Set 1 — Question 48
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Engineering Mathematics → Numerical Solution of Equations → Newton-Raphson Method
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Question
Starting with the first approximation as , the second approximation for the root of the following function by the Newton-Raphson method is ______ (rounded off to two decimal places).
Correct answer
0.55 to 0.58
Solution
Given the function .
To find the root using the Newton-Raphson method, we use the iterative formula:First, find the derivative of :Given the first approximation :
To find the root using the Newton-Raphson method, we use the iterative formula:First, find the derivative of :Given the first approximation :
1.Calculate :
2.Calculate :
3.Calculate the second approximation :
Rounding to two decimal places, we get .Continue learning with Success Tracker
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