Question

Find the three zeros for the following function on the interval -5 </= x </= 5
(1 + 50sin(x)) / (x^2 + 3)

Answer 1

For the expression to be zero,
1 + 50sinx = 0
sinx = -1/50

x = π +.02 or 2π - .02
x = 3.1616 or 6.263
the period of 50sinx is 2π, so adding or subtracting 2π to the above answers will produce more answers

3.1616+2π ---> beyond domain
3.1616-2π = -3.1216
6.263-2π = -.02
so for -5 ≤ x ≤ 5
x = -3.1216 , -.02, 3.1216

Answer 2

Thank you, this helps tremendously!

Answer 3

How did you come up with 3.1216 positive. I've tried to come up with this number but I can't figure it out. Also, it doesn't make 1 + 50 sin(x) = 0.

Answer 4

It was a copy error.
As you can see from the 5th line, I had x = 3.1616

so the final answers are
x = -3.1216 , -.02, and 3.1616