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kaylalynn
show using limits that f(x)=tan(x) is continuous at x=0
for any f(x) to be continuous at x=a, lim x->a- f(x) = f(x) = lim x->a+ f(x) what this means is, the function value at x=a must be approached from both the left and right.
So in your case of f(x) = tan(x) at x = 0, Now using what we discussed earlier, lim x->0- tan(x) = 0 since there is no problem plugging it straight in tan(0) = 0 lim x->0+ tan(x) = 0 again, plugging it straight in. Now since all three parts are equal, the function is therefore continuous at x = 0.