State division working rule of limit.

1.	State division working rule of limit.
Answer» f (x) and g (x) are two functions of real variable x and \(\lim\limits_{x\to a}\) f(x) = 1, \(\lim\limits_{x\to a}\) g (x) = m. If \(\frac{f(x)}{g(x)}\) is the division of the two functions. then division working rule of limit is as follows: \(\lim\limits_{x\to a}\,\left[\frac{f(x)}{g}(x)\right]\\=\frac{\lim\limits_{x\to a}\,f(x)}{\lim\limits_{x\to a}\,g(x)}\\=\frac{l}{m},m\neq0\) Thus, the limit of division of two functions is equal to the division of their limits, where the limit of the function in denominator is not zero.

Answer»

f (x) and g (x) are two functions of real variable x and \(\lim\limits_{x\to a}\) f(x) = 1, \(\lim\limits_{x\to a}\) g (x) = m.

If \(\frac{f(x)}{g(x)}\) is the division of the two functions. then division working rule of limit is as follows:

\(\lim\limits_{x\to a}\,\left[\frac{f(x)}{g}(x)\right]\\=\frac{\lim\limits_{x\to a}\,f(x)}{\lim\limits_{x\to a}\,g(x)}\\=\frac{l}{m},m\neq0\)

Thus, the limit of division of two functions is equal to the division of their limits, where the limit of the function in denominator is not zero.

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