How do you find if #f(x)=1/(x^2+1)# is continuous and which discontinuities are removable?

Answer 1

#x^2+1# is continuous and #> 0 AA x in RR# so also #1/(x^2+1)# is continuous in all of #RR#

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Answer 2

To determine if the function f(x) = 1/(x^2+1) is continuous, we need to check its continuity at all points in its domain. The function is continuous for all real numbers x, except for the points where the denominator (x^2+1) equals zero. Solving x^2+1 = 0, we find that there are no real solutions. Therefore, f(x) is continuous for all real numbers x, and there are no removable discontinuities.

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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.

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.

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.

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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