Determine-the-smallest-natural-value-of-n-so-the-function-y-5x-sin-5nx-will-be-even-

Question Number 4904 by love math last updated on 20/Mar/16

D e t e r m i n e t h e s m a l l e s t n a t u r a l

v a l u e o f n, s o t h e f u n c t i o n

y = 5 x s i n 5 n x w i l l b e e v e n .

Commented by Yozzii last updated on 20/Mar/16

y (- x) = 5 (- x) s i n (- 5 n x)

y (- x) = - 5 x {- s i n (5 n x)}

y (- x) = 5 x s i n 5 n x = y (x)

y (x) = y (- x) f o r a l l n, x \in R .

\Rightarrow m i n (n) = 1 \in N .

I f f (u) & h (u) a r e o d d f u n c t i o n s

t h e n f o r g (u) = f (u) h (u), g (u) i s

e v e n . h = 5 x i s o d d a n d f = s i n 5 n x

i s o d d \Rightarrow y = h \times f = 5 x s i n 5 n x i s e v e n

f o r a l l n, x \in R .

Commented by Yozzii last updated on 20/Mar/16

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