Finding Solutions to ln(x+1) = sin^2(x) on the Interval (0,3)

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SUMMARY

The discussion centers on solving the equation ln(x+1) = sin²(x) within the interval (0, 3). The user successfully identifies three solutions: 0, 0.964, and 1.684 using a calculator. The primary method suggested for solving this equation without a calculator is Newton's method, a numerical technique for finding successively better approximations to the roots of a real-valued function.

PREREQUISITES
  • Understanding of logarithmic functions, specifically ln(x+1)
  • Knowledge of trigonometric functions, particularly sin²(x)
  • Familiarity with numerical methods, especially Newton's method
  • Basic calculus concepts, including derivatives
NEXT STEPS
  • Study the application of Newton's method for root-finding problems
  • Explore the properties of logarithmic and trigonometric functions
  • Learn about numerical approximation techniques beyond Newton's method
  • Investigate the behavior of the function ln(x+1) - sin²(x) to analyze its roots
USEFUL FOR

Students in calculus, mathematicians interested in numerical methods, and anyone seeking to solve transcendental equations without relying on calculators.

tachu101
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Homework Statement



ln(X+1)=Sin^2(x) solve

The Attempt at a Solution



I can get three solutions 0, .964, 1.684 using the calculator. How do you solve this wo/ a calculator.
 
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My only thought is Newton's method.
 

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