Find the three zeros for the following function on the interval -5 </= x </= 5
(1 + 50sin(x)) / (x^2 + 3)
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
Thank you, this helps tremendously!
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.
To find the zeros of a function, we need to determine the values of x where the function equals zero. In other words, we are looking for the x-values that make the function equal to zero.
The given function is (1 + 50sin(x)) / (x^2 + 3). We need to solve the equation (1 + 50sin(x)) / (x^2 + 3) = 0.
To determine the zeros of the function, we set the numerator equal to zero and solve for x. So, we solve the equation 1 + 50sin(x) = 0.
To solve this equation, we isolate the sin(x) term. Subtracting 1 from both sides, we get 50sin(x) = -1.
Now, divide both sides of the equation by 50, which gives us sin(x) = -1/50.
To find the values of x, we need to take the inverse sine (or arcsine) of both sides. This gives us x = arcsin(-1/50).
However, we are only looking for solutions within the given interval of -5 ≤ x ≤ 5. So, we need to find the values of x when -5 ≤ x ≤ 5 that satisfy the equation sin(x) = -1/50.
Using a calculator or mathematical software, we can find the solution to be approximately x = -0.04, x = -3.1, and x = 3.1 (rounded to one decimal place).
Therefore, the three zeros of the function on the interval -5 ≤ x ≤ 5 are approximately -0.04, -3.1, and 3.1.
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