Question

The number of non-zero solutions of the equation Sinx=x.​

Answer 1

SOLUTION

TO DETERMINE

The number of non-zero solutions of the equation

$\sf{ \sin x = x}$

EVALUATION

Here the given equation is

$\sf{ \sin x = x}$

By Maclaurin Series Expansion we get

$\displaystyle \sf{ \implies \: x - \frac{ {x}^{3} }{3!} + \frac{ {x}^{5} }{5!} - \frac{ {x}^{7} }{7!} + ... = x}$

$\displaystyle \sf{ \implies \: - \frac{ {x}^{3} }{3!} + \frac{ {x}^{5} }{5!} - \frac{ {x}^{7} }{7!} + ... = 0}$

$\displaystyle \sf{ \implies \: - {x}^{3} \bigg( \: \frac{1 }{3!} - \frac{ {x}^{2} }{5!} + \frac{ {x}^{4} }{7!} + ... \: \bigg) = 0}$

$\displaystyle \sf{ \implies \: - {x}^{3} = 0}$

$\displaystyle \sf{ \implies \: x = 0}$

Thus the only solution is x = 0

∴ The number of non-zero solutions of the equation = 0

FINAL ANSWER

The number of non-zero solutions of the equation = 0

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If integral of (x^-3)5^(1/x^2)dx=k5^(1/x^2), then k is equal to?

https://brainly.in/question/15427882

2. If integral of (x^-3)5^(1/x^2)dx=k5^(1/x^2), then k is equal to?

https://brainly.in/question/15427882