Question

x^{4}(x^{2}-3)^{6}sin^{2}8x

Functions
ANSWERED
asked 2021-01-06
\(\displaystyle{x}^{{{4}}}{\left({x}^{{{2}}}-{3}\right)}^{{{6}}}{{\sin}^{{{2}}}{8}}{x}\)

Answers (1)

2021-01-07
If the question is to find the zeros of the function, then here is the answer.
We have \(\displaystyle{x}^{{{4}}}{\left({x}^{{{2}}}−{3}\right)}^{{{6}}}{{\sin}^{{{2}}}{8}}{x}={0}\) only when
\(\displaystyle{x}^{{{4}}}={0},{\quad\text{or}\quad},{x}^{{{2}}}-{3}{)}^{{{6}}}={0},{\quad\text{or}\quad},{{\sin}^{{{2}}}{8}}{x}={0}\)
This is equivalent to
\(\displaystyle{x}={0},{\quad\text{or}\quad},{x}^{{{2}}}-{3}={0},{\quad\text{or}\quad},{\sin{{8}}}{x}={0}\)
We know that sine function is zero for angles nπ,nπ, where nn is an integer. Therefore, we get
\(\displaystyle{x}={0},{\quad\text{or}\quad},{x}=\pm\sqrt{{3}},{\quad\text{or}\quad},{x}={\frac{{{8}}}{{{n}\pi}}}.\)
If you need more explanation, or wanted something else then feel free to leave a comment. I will update the answer accordingly. ​
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