Mar 2, 2014 Thread starter #1 C Cbarker1 Active member Jan 8, 2013 242 Let $f=tan(2x)/x$, x is not equal to 0. Can the f be defined at x=0 such that it is continuous? I answered yes. I am wondering if the answer is correct. Thank you for your help CBarker1
Let $f=tan(2x)/x$, x is not equal to 0. Can the f be defined at x=0 such that it is continuous? I answered yes. I am wondering if the answer is correct. Thank you for your help CBarker1
Mar 2, 2014 #2 T ThePerfectHacker Well-known member Jan 26, 2012 236 Compute limit at $0$. What do you get?
Mar 3, 2014 #4 T ThePerfectHacker Well-known member Jan 26, 2012 236 Cbarker1 said: I got 2. Click to expand... So, $$\lim_{x\to 0} \frac{\tan 2x}{x} = 2$$ Now define the function, $$ f(x) = \left\{ \begin{array}{ccc}(\tan x)/x & \text{if} & x\not = 0 \\ 2 & \text{if}& x=0 \end{array} \right. $$ This function is continous everywhere because at $0$ we have $\lim_{x\to 0}f(x) = f(0) = 2$.
Cbarker1 said: I got 2. Click to expand... So, $$\lim_{x\to 0} \frac{\tan 2x}{x} = 2$$ Now define the function, $$ f(x) = \left\{ \begin{array}{ccc}(\tan x)/x & \text{if} & x\not = 0 \\ 2 & \text{if}& x=0 \end{array} \right. $$ This function is continous everywhere because at $0$ we have $\lim_{x\to 0}f(x) = f(0) = 2$.