4 votes 4 votes Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$ Calculus gate1995 calculus limits numerical-answers + – admin asked Apr 25, 2021 admin 1.5k views answer comment Share Follow See 1 comment See all 1 1 comment reply Gajanan Purud commented Sep 16, 2023 reply Follow Share 1 0 votes 0 votes Please log in or register to add a comment.
Best answer 13 votes 13 votes $\displaystyle \lim_{x\rightarrow 0}\frac{\sin x}{x} = \displaystyle \lim_{x\rightarrow 0}\frac{\cos x}{1}$ (Applying L'Hôpital's rule since 0/0 form) $\qquad =1.$ abhi18459 answered May 5, 2016 • edited Jan 16, 2023 by shadymademe abhi18459 comment Share Follow See all 5 Comments See all 5 5 Comments reply ਜਗਮੀਤ commented Jan 26, 2017 reply Follow Share http://mathworld.wolfram.com/LHospitalsRule.html 0 votes 0 votes Sachin Mittal 1 commented Jan 31, 2017 reply Follow Share you cant apply L'Hospitals Rule here,$\lim_{x\rightarrow 0}\frac{\sin x}{x}$. bcoz to apply L'Hospitals Rule, you have to differentiate $sin(x)$, but if you see proof for, differentiation of $sin(x)$ then it uses this limit, $\lim_{x\rightarrow 0}\frac{\sin x}{x}$. The proof of $\lim_{x\rightarrow 0}\frac{\sin x}{x} = 1$ was asked once in IIT-JEE for $5$ marks. 10 votes 10 votes Abhijit Sen 4 commented Apr 15, 2018 reply Follow Share Expand Sinx =x-(x^3)/3 .. Sinx/x= 1-(X^2)/3.... Put x=0 Only 1 will remain 2 votes 2 votes anchitjindal07 commented Dec 19, 2018 reply Follow Share Sachin Mittal 1 I could not understand why u said we cant apply L Hospital's Rule. Please explain a bit more 2 votes 2 votes rohith1001 commented Sep 30, 2019 reply Follow Share https://math.stackexchange.com/a/75151/545704 2 votes 2 votes Please log in or register to add a comment.