91Ó°ÊÓ

Use numerical or graphical means to find the limit, if it exists. If the limit of f as x approaches c does exist, answer this question: Is it equal to \(f(c) ?\) $$\lim _{x \rightarrow 2} \frac{x^{2}-5 x+6}{x^{2}-6 x+8}$$

(a) Approximate \(\lim _{x \rightarrow 0}(1+x)^{1 / x}\) to seven decimal places. (Evaluate the function at numbers closer and closer to 0 until successive approximations agree in the first seven decimal places.) (b) Find the decimal expansion of \(e\) to at least nine decimal places. (c) On the basis of the results of parts (a) and (b), what do you think is the exact value of \(\lim _{x \rightarrow 0}(1+x)^{1 / x} ?\)