Chapter 11.1, Problem 3E

To determine

To evaluate three basic limits that result from direct substitution.

Explanation of Solution

Three basic limits that result from direct substitution:-

a) $\underset{x\to C}{\lim }b=b$

Limit of constant is simply the constant.

b) $\underset{x\to c}{\lim }{x}^m=c^m$

Limit of power (m) is the power of limit.

c) If limit f (x) and g (x) both exist , then

Sum : lim [ f (x) + g (x) ] = lim f (x) + lim g (x)

Difference : lim [ f (x) - g (x) ] = lim f (x) - lim g (x)

Product : lim [ f (x) * g (x) ] = lim f (x) * lim g (x)

Quotient : lim [ f (x) / g (x) ] = lim f (x) / lim g (x)