# Newton's Method

jisbon
Homework Statement:
Let $$f(x) = \begin{cases} \dfrac{x^3-1}{\sqrt{x}-1}, & x > 1\\ cos(x-1)-x^2, & x \leq 1\end{cases}$$

Use Newton's method with ##x_{0} =1##, compute the second iterate to approximate value ##c## where ##c## is a stationary value that lies in the x-axis for some ##0<c<1##
Relevant Equations:
-
Since the Newton's method is as follows:

$$x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}$$

$$x_{1}=x_{0}-\frac{cos(0)-1}{-sin(0)-2}$$

Is this correct? What should I proceed on from here?

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Mentor
Homework Statement: Let $$f(x) = \begin{cases} \dfrac{x^3-1}{\sqrt{x}-1}, & x > 1\\ cos(x-1)-x^2, & x \leq 1\end{cases}$$

Use Newton's method with ##x_{0} =1##, compute the second iterate to approximate value ##c## where ##c## is a stationary value that lies in the x-axis for some ##0<c<1##
Homework Equations: -

Since the Newton's method is as follows:

$$x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}$$

$$x_{1}=x_{0}-\frac{cos(0)-1}{-sin(0)-2}$$

Is this correct?
Yes, as far as you went
jisbon said:
What should I proceed on from here?
Evaluate cos(0) and sin(0) and substitute in the value for ##x_0##.