How do you solve this problem step by step?

Let  #f(x)=x^3-8 divide x-2# This function has a removable discontinuity at x=2 (but is continuous at all other real numbers). How should this function be re-defined at x=2 in order for the function to be continuous everywhere?

Answer 1

Use #x^3-2^3=(x-2)(x^2+2x+4)# to reduce and find the limit as #xrarr2#.

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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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