Answer
1) The limit on a sum is equal to the sum of the limits.
2) The limit on a product is equal to the product of the limits.
3) The limit on a quotient is equal to the quotient of the limits,
provided the limit of the denominator is not 0.
4) The limit on a constant is constant itself.
5) The limit on product of constant and variable is equal to product of constant with limit on the variable.
Work Step by Step
If,
$ \lim\limits_{x \to a} f = A and \lim\limits_{x \to a} g = B $
1) $ \lim\limits_{x \to a} (f+g) = A +B $
2) $ \lim\limits_{x \to a} (f\times g) = AB $
3) $ \lim\limits_{x \to a} (\frac{A}{B}) = \frac{A}{B} where B\ne 0$
4) $ \lim\limits_{x \to a} c = c $
5) $ \lim\limits_{x \to a} (cf) = A $
