A) \[2\pi \]
B) \[10\pi \]
C) \[8\pi \]
D) \[5\pi \]
Correct Answer: D
Solution :
\[f(x)=\left| {{\sin }^{3}}\frac{x}{2} \right|+\left| {{\cos }^{5}}\frac{x}{5} \right|\] Period of \[{{\sin }^{3}}x\]is\[2\pi \]. \[\Rightarrow \] Period of\[{{\sin }^{3}}\frac{x}{2}\]is\[\frac{2\pi }{1/2}=4\pi \]. \[\Rightarrow \] Period of\[\left| {{\sin }^{3}}\frac{x}{2} \right|\]is\[2\pi \]. Period of\[{{\cos }^{5}}x\]is\[2\pi \]. \[\Rightarrow \] Period of\[{{\cos }^{5}}\frac{x}{2}\]is\[\left( \frac{2\pi }{1/5} \right)=10\pi \] \[\Rightarrow \] Period of\[\left| {{\cos }^{5}}\frac{x}{2} \right|\]is\[5\pi \]. Now, period of\[f(x)=\]LCM of\[\{2\pi ,\,\,10\pi \}=10\pi \]
You need to login to perform this action.
You will be redirected in
3 sec
