# Thread: limit of a trig function

1. ## limit of a trig function

Hi. I'm just a little confused about something.

Here is the problem,

limit as x approaches 0, of tan(pi/4(cos(sin x^(1/3))

So it's simple, cube root of 0 is 0, and sin 0 is 0, cos of 0 is 1, and so pi/4*1=pi/4.

So the limit is tan(pi/4), which is 1.

They ask if the function is continuous at this point, x=0. According to my calculator, at x=0, f(x)=.999999999999999...

I'm just not sure what this means. Does the point x=0, y=1 exist for this function?

2. ## Re: limit of a trig function

Originally Posted by StudentMCCS
Here is the problem,

limit as x approaches 0, of tan(pi/4(cos(sin x^(1/3))

So it's simple, cube root of 0 is 0, and sin 0 is 0, cos of 0 is 1, and so pi/4*1=pi/4.

So the limit is tan(pi/4), which is 1.

They ask if the function is continuous at this point, x=0.
Does $\displaystyle f(0)$ exist?
Does $\displaystyle \lim _{x \to 0} f(x) = f(0)~?$

If you answer yes to both questions then $\displaystyle f$ is continuous at $\displaystyle x=0$.

3. ## Re: limit of a trig function

Originally Posted by Plato
Does $\displaystyle f(0)$ exist?
Does $\displaystyle \lim _{x \to 0} f(x) = f(0)~?$

If you answer yes to both questions then $\displaystyle f$ is continuous at $\displaystyle x=0$.
According to my math, yes. But according to my calculator no. This is what I don't understand, why does the calculator say f(o)=.9999999, when it should say 1?

4. ## Re: limit of a trig function

Originally Posted by StudentMCCS
According to my math, yes. But according to my calculator no. This is what I don't understand, why does the calculator say f(o)=.9999999, when it should say 1?
Throw calculators away. They are useless for limits.

5. ## Re: limit of a trig function

Thanks Plato.