Math Help - First year Calculus question

I hate math, and suck at it, but I have to do it. I'm stuck on only one question on my current assignment. It looks really simple, but I've tried it a couple different ways, and I end up hitting a brick wall. Here it is;

2. Does the equation 3x^3 - sin(x) + 3 = 0 have a solution?

I haven't been able to find a value for x, and if it doesn't have a solution, I'm not sure how to show that... Can anyone help?

We've been mostly dealing with limits so far, so this question kind of threw me for a loop. I'm not sure how to isolate x...

Hello, Sucker Punch!

2. Does the equation 3x³ - sin(x) + 3 = 0 have a solution?

If that's the exact question, they did not ask for the solution(s).
If they want a Yes-or-No answer, the answer is: Yes.

We cannot solve for x; we can only approximate the value.

We have: .3x³ + 3 .= .sin(x)
. . and we want the intersection(s) of the curves: .y = 3x³ + 3 .and .y = sin(x).

If we sketch the two graphs, we find an intersection in Quadrant 3.

aw geez, you're right.

It isn't even asking for a value. Thanks so much, this has been driving me out of my mind.

I should have known too, we've been dealing with continous functions, and a lot of that is determining whether there is a proper answer or not.