Answer to Question #301575 in Calculus for sakshi

Question

discuss the continuity of function f(={sin x/x and 1 at x=0

Answer 1

If $x=c\not=0$

$$\lim\limits_{x\to c}f(x)=\lim\limits_{x\to c}\dfrac{\sin x}{x}=\dfrac{\sin c}{c}=f(c)$$

If $x=0$

$$\lim\limits_{x\to 0}f(x)=\lim\limits_{x\to 0}\dfrac{\sin x}{x}=1=f(0)$$

The function $f(x)$ is continuous for $x\in \R.$