Math  /  Trigonometry

QuestionThe curve y=tanx\mathrm{y}=\tan \mathrm{x} crosses the line y=6x\mathrm{y}=6 \mathrm{x} at a non-zero x -value between x=0\mathrm{x}=0 and x=π2\mathrm{x}=\frac{\pi}{2}. Use Newton's method to find where the curves intersect. Compute successive approximations to find the solution to seven decimal places.
The curve y=tanxy=\tan x crosses the line y=6xy=6 x at x=x= \square . (Type an integer or decimal rounded to seven decimal places as needed.)

Studdy Solution
Check for convergence to seven decimal places:
- Ensure that the difference between successive approximations is less than 107 10^{-7} .
The curve y=tanx y = \tan x crosses the line y=6x y = 6x at x=0.1675835 x = \boxed{0.1675835} .

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