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Equation ex - 1 = 0 is required to be solved using Newton's method with an initial guess x0 = -1. Then, after one step of Newton’s method, estimate x1 of the solution will be given by
  • a)
    0.71828
  • b)
    0.36784
  • c)
    0.20587
  • d)
    0.00000
Correct answer is option 'A'. Can you explain this answer?
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Equation ex - 1 = 0 is required to be solved using Newton's method...

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Equation ex - 1 = 0 is required to be solved using Newton's method...
To solve the equation x^2 - 1 = 0 using Newton's method, we need to find the root of the equation by iteratively improving our initial guess.

First, let's find the derivative of the equation:
f(x) = x^2 - 1
f'(x) = 2x

Newton's method formula is given by:
x1 = x0 - f(x0)/f'(x0)

Given x0 = -1, let's substitute it into the formula:
x1 = -1 - (-1^2 - 1)/(2(-1))
= -1 - (1 - 1)/(-2)
= -1 - 0/(-2)
= -1

So, after one step of Newton's method, the new approximation is x1 = -1.
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