Maths-
General
Easy

Question

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

  1. Periodic with period pi
  2. Periodic with period 2pi
  3. Periodic with period 0
  4. Not a Periodic function Extreme Values:

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 fromopen 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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equals open parentheses cos space open parentheses 60 plus x close parentheses plus cos open parentheses 60 minus x close parentheses close parentheses squared minus 2 cos space open parentheses 60 minus x close parentheses. cos space open parentheses 60 plus x close parentheses
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equals cos squared x minus 2 cos squared x plus 1 plus 1 half
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    parallel

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