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anonymous
 2 years ago
show using limits that f(x)=tan(x) is continuous at x=0
anonymous
 2 years ago
show using limits that f(x)=tan(x) is continuous at x=0

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anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0for 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.

anonymous
 2 years ago
Best ResponseYou've already chosen the best response.0So 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.
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