Q. 3 State the constant multiple rule... [FREE SOLUTION]

Chapter 1: Q. 3 (page 135)

State the constant multiple rule, sum rule, product rule, quotient rule, and composition rule for limits.

Expert verified

The constant multiple rule is $\lim_{x 鈫� c} k f (x) = k \lim_{x 鈫� c} f (x)$ .

The sum rule is $\lim_{x 鈫� c} [f (x) + g (x)] = \lim_{x 鈫� c} f (x) + \lim_{x 鈫� c} g (x)$ .

The product rule is $\lim_{x 鈫� c} [f (x) g (x)] = \lim_{x 鈫� c} f (x) \lim_{x 鈫� c} f (x)$ .

The quotient rule is $\lim_{x 鈫� c} \frac{f (x)}{g (x)} = \frac{\lim_{x 鈫� c} f (x)}{\lim_{x 鈫� c} g (x)}; g (x) 鈮� 0$ .

The composition rule for limits is $\lim_{x 鈫� c} f [g (x)] = f (\lim_{x 鈫� c} g (x))$ , where f is continuous at $\lim_{x 鈫� c} g (x)$ .

We have to write sum rule, constant rule, product rule, quotient rule, and composition rule for limits.

The constant multiple rule is $\lim_{x 鈫� c} k f (x) = k \lim_{x 鈫� c} f (x)$ .

The sum rule is $\lim_{x 鈫� c} [f (x) + g (x)] = \lim_{x 鈫� c} f (x) + \lim_{x 鈫� c} g (x)$ .

The product rule is $\lim_{x 鈫� c} [f (x) g (x)] = \lim_{x 鈫� c} f (x) \lim_{x 鈫� c} f (x)$ .

The quotient rule is $\lim_{x 鈫� c} \frac{f (x)}{g (x)} = \frac{\lim_{x 鈫� c} f (x)}{\lim_{x 鈫� c} g (x)}; g (x) 鈮� 0$ .

The composition rule for limits is $\lim_{x 鈫� c} f [g (x)] = f (\lim_{x 鈫� c} g (x))$ , where f is continuous at $\lim_{x 鈫� c} g (x)$ .

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