Define the function at "a" so as to make it continuous at "a"

[From: ] [author: ] [Date: 11-12-21] [Hit: ]

you need to find the limit of f(x) as x approaches a = 0. In this case what you do is use LHôpitals rule and differentiate both the numerator and denominator of f(x). You should get sec^2(x), and the limit of sec^2(x) at x = a = 0 is 1. This means that the limit of f(x) at x = a = 0 is 1, which you can now use to define f(x) at a to make it continuous.......

f(x) = tanx/x a=0

i cant get the answer. the answer is 1
i tried making it sin/cos but i still couldn't get the answer

ten points to whoever can explain and help thanks!

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To define f(x) at a, you need to find the limit of f(x) as x approaches a = 0. In this case what you do is use L'Hôpital's rule and differentiate both the numerator and denominator of f(x). You should get sec^2(x), and the limit of sec^2(x) at x = a = 0 is 1. This means that the limit of f(x) at x = a = 0 is 1, which you can now use to define f(x) at a to make it continuous.

1

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