91Ó°ÊÓ

In Exercises 39-48, write the first five terms of the sequence and find the limit of the sequence (if it exists). If the limit does not exist, explain why. Assume \(n\) begins with 1. $$ a_n = \dfrac{n}{2n+1} $$

GRAPHICAL, NUMERICAL, AND ALGEBRAIC ANALYSIS In Exercises 49-54, (a) graphically approximate the limit (if it exists) by using a graphing utility to graph the function, (b) numerically approximate the limit (if it exists) by using the \(table\) feature of a graphing utility to create a table, and (c) algebraically evaluate the limit (if it exists) by the appropriate technique(s). $$\lim_{x \to 5^+} \dfrac{5-x}{25-x^2}$$

Describe the process of finding the area of a region bounded by the graph of a nonnegative, continuous function \( f \), the \(x\)-axis, and the vertical lines \(x = a\) and \(x = b\).

TRUE OR FALSE? In Exercises 85 and 86, determine whether the statement is true or false. Justify your answer. When your attempt to find the limit of a rational function yields the indeterminate form \(\frac{0}{0}\) the rational function's numerator and denominator have a common factor.