Question

lim x-sinx/x+sinx=?
x->0

Answer 1

plz help me!!

Answer 2

\[\lim_{x\to0}\frac{x-\sin(x)}{x+\sin(x)}=\lim_{x\to0}\frac{1-\cos(x)}{1+\cos(x)}.\]Does that make it easier?

(L'Hôpital's rule)

Answer 3

gj across

Answer 4

lets see if we can do it without L'Hopital's way
\[\lim_{x \rightarrow 0}\frac{x-\sin(x)}{x+\sin(x)} \cdot \frac{\frac{1}{x}}{\frac{1}{x}}\]
\[=\lim_{x \rightarrow 0}\frac{1-\frac{\sin(x)}{x}}{1+\frac{\sin(x)}{x}}=\frac{1-1}{1+1}=0/2=0\]

Answer 5

thanks a alot!