91Ó°ÊÓ

What do you think is the appropriate limit of each sequence? a. \(0.7,0.72,0.727,0.7272, \ldots\) b. \(3,3.1,3.14,3.141,3.1415,3.14159,3.141592, \ldots\)

Write the conjugate of each radical expression. a. \(2 \sqrt{3}-4\) b. \(\sqrt{3}+\sqrt{2}\) c. \(-2 \sqrt{3}-\sqrt{2}\) d. \(3 \sqrt{3}+\sqrt{2}\) e. \(\sqrt{2}-\sqrt{5}\) f. \(-\sqrt{5}+2 \sqrt{2}\)

The velocity of an object is given by \(v(t)=t(t-4)^{2} .\) At what times, in seconds, is the object at rest?

$$\text { Are there different answers for } \lim _{x \rightarrow 2}(3+x), \lim _{x \rightarrow 2} 3+x, \text { and } \lim _{x \rightarrow 2}(x+3) ?$$

Calculate the slope of the line through each pair of points. a. (2,7),(-3,-8) b. \(\left(\frac{1}{2}, \frac{3}{2}\right),\left(\frac{7}{2},-\frac{7}{2}\right)\) c. (6.3,-2.6),(1.5,-1)

Give a geometrical interpretation of the following expressions, if \(s\) is a position function: $$\text { a. } \frac{s(9)-s(2)}{7}$$ $$\text { b. } \lim _{h \rightarrow 0} \frac{s(6+h)-s(6)}{h}$$

Determine the slope of a line perpendicular to each of the following: a. \(y=3 x-5\) b. \(13 x-7 y-11=0\)

Rationalize the denominator of each expression. Write your answer in simplest form. a. \(\frac{\sqrt{3}+\sqrt{5}}{\sqrt{2}}\) b. \(\frac{2 \sqrt{3}-3 \sqrt{2}}{\sqrt{2}}\) c. \(\frac{4 \sqrt{3}+3 \sqrt{2}}{2 \sqrt{3}}\) d. \(\frac{3 \sqrt{5}-\sqrt{2}}{2 \sqrt{2}}\)

What does it mean for a function to be continuous over a given domain?

$$\text { Once you know } \lim _{x \rightarrow a^{-}} f(x) \text { and } \lim _{x \rightarrow a^{+}} f(x), \text { do you then know } \lim _{x \rightarrow a} f(x) ?$$ Give reasons for your answer.