Let f, g, and h be the functions defined by f (æ) h (x) 1-cos # g (x) = x² sin (G), and x2 sin æ for x + 0. All of the following inequalities are true for x 0. Which of the inequalities can be used with the squeeze theorem to find the limit of the function as x approaches 0 ? 1. (1 – a²) < f (æ) < II. –x? < g (x)< x² 1. |x|

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.