Question

lim log(1+sinx)/x
X-0​

Answer 1

Question :-

$\lim _{x→0} \sf \frac{ log(1 + \sin x) }{x}$

Answer :-

Using Property :-

$\to \boxed{\lim _{x→0} \sf \frac{ log(1 + x) }{x} = 1 }\\ \\ \to \boxed{\lim _{x→0} \sf \frac{\sin x }{x} = 1}$

Solution :-

We have

$\to \: \lim _{x→0} \sf \frac{ log(1 + \sin x) }{x}$

to make it like its property we have to multiply and divide by sin x

$\to \: \lim _{x→0} \sf \frac{ \sin x \: \: \: \: \{log(1 + \sin x) \}}{x \sin x} \\ \: \\ \\ \to \sf \: \lim _{x→0} \sf \frac{ \sin x }{x} \\ \: = 1$