91Ó°ÊÓ

Geometry A right triangle has a hypotenuse of \(\sqrt{18 \text { inches. }}\) (a) Draw and label a diagram that shows the base \(x\) and height \(y\) of the triangle. (b) Write a function \(A(x)\) that represents the area of the triangle. (c) The triangle has a maximum area when \(x=3\) inches. Use a graphing utility to complete the table and observe the behavior of the function as \(x\) approaches 3\. Use the table to find \(\lim _{x \rightarrow 3} A(x)\) (d) Use the graphing utility to graph the area function. Verify that the area is maximum when \(x=3\) inches.

The limit of a _____ _____ is an expression of the form \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\)

Fill in the blanks. The slope of the tangent line to a graph at \((x, f(x))\) is given by ______ .

Estimating a Limit Numerically In Exercises \(5-10\) , complete the table and use the result to estimate the limit numerically. Determine whether it is possible to reach the limit. $$\lim _{x \rightarrow 2}(5 x+4)$$

Evaluating a Summation, evaluate the sum using the summation formulas and properties. $$\sum_{i=1}^{60} 7$$

Estimating a Limit Numerically In Exercises \(5-10\) , complete the table and use the result to estimate the limit numerically. Determine whether it is possible to reach the limit. $$\lim _{x \rightarrow-1}\left(2 x^{2}+x-4\right)$$

Evaluating a Summation, evaluate the sum using the summation formulas and properties. $$\sum_{i=1}^{45} 3$$

Finding a Limit, find the limit (if it exists. Use a graphing utility to verify your result graphically. $$ \lim _{x \rightarrow 6} \frac{x-6}{x^{2}-36} $$

Evaluating a Summation, evaluate the sum using the summation formulas and properties. $$\sum_{i=1}^{20} i^{3}$$

Estimating a Limit Numerically In Exercises \(5-10\) , complete the table and use the result to estimate the limit numerically. Determine whether it is possible to reach the limit. $$\lim _{x \rightarrow-3} \frac{x+3}{x^{2}-9}$$