# The graph of h(x) is shown. The graph appears to be continuous at , where the definition changes. Show that h is in fact continuous at by finding the left and right limits and showing that the definition of continuity is met?

Kindly refer to the Explanation.

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For a function to be continuous at a point (call it 'c'), the following must be true:

The former is defined to be true, but we'll need to verify the latter. How? Well, recall that for a limit to exist, the right and left hand limits must equal the same value. Mathematically:

This is what we'll need to verify:

Now, we just evaluate these limits, and check if they're equal:

Hope that helped :)

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