To calculate: The roots of the curve,
The roots are
The infinitely many lines that are tangent to the curve passes through the origin.
We seek a solution of , starting from an initial estimate .
For , compute the next approximation by
and so on.
Equation of tangent line :
Slope of the tangent line : derivative of the function.
Consider the curve ,
The line passes through the origin
While the tangent will touch the curve at some point. Let the x -coordinate be a.
Therefore , putting x-coordinate in equation we get,
The point at which tangent touches the curve is .
Put it in equation (i)
Slope of the tangent :-
At point the slope will be
We get ,
Sketching the graph of function and . We observe the graph is symmetric.
Hence, we get the slope of the curve is . In other words used to find out roots using Newton’s Method.
Now, let initial approximation be
The second approximation is .
The third approximation is .
Hence , the roots of the curve are :-
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