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Which of the following is not a periodic function -
[AIEEE 2002]
- a)sin 2x + cos x
- b)cos √x
- c)tan 4x
- d)log cos 2x
Correct answer is option 'B'. Can you explain this answer?
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Which of the following is not a periodic function -[AIEEE 2002]a)sin 2...
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Periodic Functions:
Periodic functions are functions that repeat their values at regular intervals. Mathematically, a function f(x) is periodic if there exists a real number T such that for all x in the domain of f, f(x+T) = f(x).
Given Functions:
a) sin 2x + cos x
b) cos x
c) tan 4x
d) log cos 2x
Explanation:
- The function sin 2x + cos x is periodic because both sin 2x and cos x are periodic functions with periods of π and 2π respectively. The sum of two periodic functions is also periodic.
- The function cos x is not periodic. It is a periodic function itself with a period of 2π. Since it does not repeat its values at regular intervals, it is not a periodic function.
- The function tan 4x is periodic because the tangent function has a period of π. Multiplying the input by 4 changes the period to π/4, making it a periodic function.
- The function log cos 2x is periodic because the cosine function has a period of 2π. Multiplying the input by 2 changes the period to π, making it a periodic function.
Conclusion:
Therefore, the function cos x is not a periodic function among the given options.
Periodic functions are functions that repeat their values at regular intervals. Mathematically, a function f(x) is periodic if there exists a real number T such that for all x in the domain of f, f(x+T) = f(x).
Given Functions:
a) sin 2x + cos x
b) cos x
c) tan 4x
d) log cos 2x
Explanation:
- The function sin 2x + cos x is periodic because both sin 2x and cos x are periodic functions with periods of π and 2π respectively. The sum of two periodic functions is also periodic.
- The function cos x is not periodic. It is a periodic function itself with a period of 2π. Since it does not repeat its values at regular intervals, it is not a periodic function.
- The function tan 4x is periodic because the tangent function has a period of π. Multiplying the input by 4 changes the period to π/4, making it a periodic function.
- The function log cos 2x is periodic because the cosine function has a period of 2π. Multiplying the input by 2 changes the period to π, making it a periodic function.
Conclusion:
Therefore, the function cos x is not a periodic function among the given options.
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Which of the following is not a periodic function -[AIEEE 2002]a)sin 2x + cos xb)cos xc)tan 4xd)log cos 2xCorrect answer is option 'B'. Can you explain this answer?
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