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Maths-

General

Easy

Question

The function $sin space open parentheses x squared close parentheses$ $plus cos space square root of x$ is

Periodic with period $π$
Periodic with period 2 $π$
Periodic with period 0
Not a Periodic function Extreme Values:

hint Hint:

In this question we have to find the correct option. As we know sin x and cos x are periodic functions only when x varies from $open parentheses negative infinity comma infinity close parentheses$ .

The correct answer is: Not a Periodic function Extreme Values:

$f left parenthesis x right parenthesis equals sin left parenthesis x squared right parenthesis plus cos square root of x sin x space i s space p e r i o d i c space f u n c t i o n space w h e n space x space v a r i e s space f r o m space minus infinity space t o space infinity. S o comma space f left parenthesis x right parenthesis equals sin left parenthesis x squared right parenthesis comma space x squared greater or equal than 0 H e r e comma space x squared space v a r i e s space f r o m space 0 space t o space infinity S o comma space sin left parenthesis x squared right parenthesis space i s space n o t space a space p e r i o d space f u n c t i o n. S i m i l a r l y comma space f left parenthesis x right parenthesis equals cos open parentheses square root of x close parentheses comma square root of x greater or equal than 0 comma space x greater or equal than 0 H e r e square root of x space v a r i e s space f r o m space 0 space t o space infinity. S o comma space cos square root of x space i s space n o t space a space p e r i o d i c space f u n c t i o n. l e t space g left parenthesis x right parenthesis equals sin left parenthesis x squared right parenthesis plus cos square root of x d o m a i n space o f space g left parenthesis x right parenthesis equals x element of left square bracket 0 comma infinity right parenthesis f o r space p e r i c space f u n c t i o n comma space d o m a i n space o f space f u n c t i o n space s h o u l d space b e space i n space left parenthesis negative infinity comma infinity right parenthesis t h i s space i m p l i e s space t h a t space g left parenthesis x right parenthesis space i s space n o t space a space p e r i o d i c space f u n c t i o n.$

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