The function f x = 2 cos ⁡ 5 x + 3 sin ⁡ 5 x is

A periodic function with period 2 π

A periodic function with period 2 π 5

The function f x = sin π x n ! − cos π x n + 1 ! is

periodic, with period 2 n + 1 !

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The function $f (x) = 2 \cos 5 x + 3 \sin \sqrt{5} x$ is

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Important Questions on Functions

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The function $f (x) = |sin 4 x| + |cos 2 x|,$ is a periodic function with a fundamental period

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

f (a + x) = f (x)

, then

\int_{0}^{n a} f (x) d x

, where

n \in N

, is equal to

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

g (x) = 5 \cot (\frac{π}{3} x + \frac{π}{6}) + 2

is equal to

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The function

f (x) = \sin (\frac{π x}{n!}) - \cos (\frac{π x}{(n + 1)!})

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

a, b

be two fixed positive integers such that

f (a + x) = b + {[b^{3} + 1 - 3 b^{2} f (x) + 3 b {\{f (x)\}}^{2} - {\{f (x)\}}^{3}]}^{1 / 3}

for all real

x

then

f (x)

is a periodic function with period

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

Consider the function

f (x) = \cos x^{2}

. Then

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

f (x) = \cos 4 x + \tan 3 x

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The function

f (x) = \tan π x - x + [x]

has period, where

[.]

denotes greatest integer function

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

f : R \to R

is a function satisfying

f (2 x + 3) + f (2 x + 7) = 2 \forall x \in R

, then the period of

f (x)

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

Let $f (x) = \sin x + \cos a x$ be a periodic function. Then,

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of

\sin^{2} θ

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of

\sin^{2} θ

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

f (x) = 2^{s i n^{3} π x + x - [x]}

, where

[\cdot]

denotes the integral part of

x

is a periodic function with period

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

f (x) = [\sin 3 x] + |\cos 6 x|

is (

[.]

denotes the greatest integer less than or equal to

x

)

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

f (x) = {(- 1)}^{[\frac{2 x}{π}]}, g(x) = |sin x| - |cos x|

and

ϕ (x) = f (x) \cdot g (x)

(where,

[.]

denote the greatest integer function), then the respective fundamental periods of

f (x), g (x)

and

ϕ (x)

are

EASY

Mathematics>Differential Calculus>Functions>Periodic Functions

The fundamental period of the function

f (x) = |\sin x| + |\cos x|

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

The period of the function

f (θ) = \sin \frac{θ}{3} + \cos \frac{θ}{2}

HARD

Mathematics>Differential Calculus>Functions>Periodic Functions

f (3 x + 2) + f (3 x + 29) = 0 \forall x \in R

, then the period of

f (x)

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

\sin a x + \cos a x

and

|\sin x| + |\cos x|

are periodic with the same fundamental period, if

a

equals to

MEDIUM

Mathematics>Differential Calculus>Functions>Periodic Functions

If the periods of the periodic functions

s i n a x + c o s a x

and

|s i n x| + |c o s x|

are equal, then

a

is equal to

The function fx=2cos⁡5x+3sin⁡5x is

Important Questions on Functions

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The function $f (x) = 2 \cos 5 x + 3 \sin \sqrt{5} x$ is