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Why is the lim(h->0) of h = 0?

I'm new to this so I'm probably being thrown by the change in variable? Is it because we assume f is a function of h, f(h) = h which we know is continous from other proofs elsewhere, which gives

lim(h->0) f(h) = f(0)

lim(h->0) h = 0

thanks

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# Homework Help: Basic limit question (limit of h as h approach 0)

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