Chapter 10 - Thomas Calculus Solutions — Page 13

Problem 146

Use a CAS to perform the following steps for the sequences in Exercises $137-148 .$ a. Calculate and then plot the first 25 terms of the sequence. Does the sequence appear to be bounded from above or below? Does it appear to converge or diverge? If it does converge, what is the limit L? b. If the sequence converges, find an integer $N$ such that $\quad\left|a_{n}-L\right| \leq 0.01$ for $n \geq N .$ How far in the sequence do you have to get for the terms to lie within 0.0001 of $L ?$ $$ a_{n}=(123456)^{1 / n} $$

6 step solution

Problem 147

Use a CAS to perform the following steps for the sequences in Exercises $137-148 .$ a. Calculate and then plot the first 25 terms of the sequence. Does the sequence appear to be bounded from above or below? Does it appear to converge or diverge? If it does converge, what is the limit L? b. If the sequence converges, find an integer $N$ such that $\quad\left|a_{n}-L\right| \leq 0.01$ for $n \geq N .$ How far in the sequence do you have to get for the terms to lie within 0.0001 of $L ?$ $$ a_{n}=\frac{8^{n}}{n !} $$

7 step solution

Problem 148

Use a CAS to perform the following steps for the sequences in Exercises $137-148 .$ a. Calculate and then plot the first 25 terms of the sequence. Does the sequence appear to be bounded from above or below? Does it appear to converge or diverge? If it does converge, what is the limit L? b. If the sequence converges, find an integer $N$ such that $\quad\left|a_{n}-L\right| \leq 0.01$ for $n \geq N .$ How far in the sequence do you have to get for the terms to lie within 0.0001 of $L ?$ $$ a_{n}=\frac{n^{41}}{19^{n}} $$

6 step solution