Question

DISCUSS THE CONTINUITY OF THE FUNCTION f (x)=tan x​

Answer 1

Let f(x) = tanx

$\implies\sf f(x)=\dfrac{sin\:x}{cos\:x}$  

​f(x) is defined for all real numbers except cosx = 0 $\implies\sf x=(2n+1)\dfrac{\pi}{2}$

Let,

• $\sf p(x)=sin\:x$

• $\sf q(x)=cos\:x$

We know,

• sinx and cosx are continuous for all real numbers which means that p(x) and q(x) is continuous.

• If p(x) and q(x) both continuous for  all real numbers then $\sf f(x) =\dfrac{p(x)}{q(x)}$ is continuous for all real numbers : $\sf q(x) \not =0$.

So,

$\sf f(x) =\dfrac{p(x)}{q(x)}$ is continuous for  all real numbers : $\sf cos\:x \not =0$ , $\sf x\not=(2n+1)\dfrac{\pi}{2}$ .

Therefore,

$\boxed{\bold{\sf tan\:x \:is \:continuous \:at \:all \:real \:numbers \:except \:\:\: x\not=(2n+1)\dfrac{\pi}{2}}}$

Answer 2

Answer:

the answer is absolutely correct

Step-by-step explanation:

so so you can see the above answer