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What is the domain of #sqrt(4-x^2)#?

Answer 1

Liam Brennan

#color(blue)([-2,2]#

If:

#sqrt(4-x^2)# is defined only for real numbers then:

#4-x^2>= 0#

#x^2<= 4#

#x<=2#

#x>=-2#

#:.#

Domain:

#[-2,2]#

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Answer 2

Theodore Amidon

#-2 <= x <= 2#

The square roots are only defined when the expression under the square root is non-negative.

#4 - x^2 >=0# #|x| <= 2# #-2 <= x <= 2#

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Answer 3

Theodore Amidon

The domain of sqrt(4-x^2) is all real numbers such that -2 ≤ x ≤ 2.

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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.