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Is the function #f(x) =x sin x# even, odd or neither?

Answer 1

Chloe Alexander

That function is even.

We will need to recall that #sinx# is odd. That is: #sin(-x) = -sinx#

#f(x) =x sin x#

For any #x# in the domain of #f# (which is #(-oo,oo)#), we get

#f(-x) =(-x) sin (-x)#

# = (-x)(-sinx)#

# = xsinx#

# = f(x)#

By the definition of even function, #f# is even.

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Answer 2

Madelyn Anderson

The function ( f(x) = x \sin(x) ) is neither even nor odd.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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