(a) Explanation Given: The sequence is given, a n = n n 2 + 4 Calculation: Limit the both sides of the sequence to the infinity, lim n → ∞ a n = lim n → ∞ n n 2 + 4 Divide the numerator and denominator of rational function by the highest power of n to solve the limit, lim n → ∞ n n 2 + 4 = lim n → ∞ n n 2 n 2 n 2 + 4 n 2 = lim n → ∞ 1 n (b) To determine To find: The limit of the sequence a n = sec n π

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

7th Edition

ISBN: 9781305618152

Author: Lothar Redlin, Saleem Watson, James Stewart

Publisher: CENGAGE C

See similar textbooks

Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 13, Problem 6T

(a)

To determine

To find: The limit of the sequence an=nn2+4 .

(b)

To determine

To find: The limit of the sequence an=secnπ

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13, Problem 5T

Chapter 13, Problem 7T

Students have asked these similar questions

j) f) lim x+x ex g) lim Inx h) lim x-5 i) lim arctan x x700 lim arctanx 811x

4. Evaluate the following integrals. Show your work. a) -x b) f₁²x²/2 + x² dx c) fe³xdx d) [2 cos(5x) dx e) √ 35x6 3+5x7 dx 3 g) reve √ dt h) fx (x-5) 10 dx dt 1+12

I just need help with evaluating these limits.

Chapter 13 Solutions

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

Ch. 13.1 - When we write limxaf(x)=L then, roughly speaking,...Ch. 13.1 - We write limxaf(x)=L and say that the ______ of...Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Ch. 13.1 - Prob. 11E Ch. 13.1 - Prob. 12E Ch. 13.1 - Prob. 13E Ch. 13.1 - Estimating Limits Numerically and Graphically Use...Ch. 13.1 - Prob. 15E Ch. 13.1 - Prob. 16E Ch. 13.1 - Prob. 17E Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Limits from a Graph For the function f whose graph...Ch. 13.1 - Prob. 21E Ch. 13.1 - Prob. 22E Ch. 13.1 - Prob. 23E Ch. 13.1 - Estimating Limits Graphically Use a graphing...Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.1 - Prob. 27E Ch. 13.1 - Prob. 28E Ch. 13.1 - Prob. 29E Ch. 13.1 - One-Sided Limits Graph the piecewise-defined...Ch. 13.1 - Prob. 31E Ch. 13.1 - Prob. 32E Ch. 13.1 - Prob. 33E Ch. 13.1 - DISCUSS: Graphing Calculator Pitfalls (a)...Ch. 13.2 - Suppose the following limits exist:...Ch. 13.2 - If f is a polynomial or a rational function and a...Ch. 13.2 - Limits from a Graph The graphs of f and g are...Ch. 13.2 - Prob. 4E Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 6E Ch. 13.2 - Prob. 7E Ch. 13.2 - Prob. 8E Ch. 13.2 - Prob. 9E Ch. 13.2 - Prob. 10E Ch. 13.2 - Prob. 11E Ch. 13.2 - Prob. 12E Ch. 13.2 - Prob. 13E Ch. 13.2 - Prob. 14E Ch. 13.2 - Prob. 15E Ch. 13.2 - Prob. 16E Ch. 13.2 - Prob. 17E Ch. 13.2 - Using Limit Laws Evaluate the limit and justify...Ch. 13.2 - Prob. 19E Ch. 13.2 - Prob. 20E Ch. 13.2 - Prob. 21E Ch. 13.2 - Prob. 22E Ch. 13.2 - Prob. 23E Ch. 13.2 - Prob. 24E Ch. 13.2 - Prob. 25E Ch. 13.2 - Prob. 26E Ch. 13.2 - Prob. 27E Ch. 13.2 - Prob. 28E Ch. 13.2 - Prob. 29E Ch. 13.2 - Prob. 30E Ch. 13.2 - Prob. 31E Ch. 13.2 - Prob. 32E Ch. 13.2 - Prob. 33E Ch. 13.2 - Prob. 34E Ch. 13.2 - Prob. 35E Ch. 13.2 - Prob. 36E Ch. 13.2 - Prob. 37E Ch. 13.2 - Prob. 38E Ch. 13.2 - Prob. 39E Ch. 13.2 - Prob. 40E Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Find the limit, if it...Ch. 13.2 - Does the Limit Exist? Let f(x)={x1ifx2x24x+6ifx2...Ch. 13.2 - Prob. 44E Ch. 13.2 - Finding Limits Numerically and Graphically (a)...Ch. 13.2 - Prob. 46E Ch. 13.2 - Prob. 47E Ch. 13.2 - Prob. 48E Ch. 13.2 - DISCUSS PROVE: Limits of Sums and Products (a)...Ch. 13.3 - The derivative of a function f at a number a is...Ch. 13.3 - Prob. 2E Ch. 13.3 - Prob. 3E Ch. 13.3 - Prob. 4E Ch. 13.3 - Prob. 5E Ch. 13.3 - Prob. 6E Ch. 13.3 - Prob. 7E Ch. 13.3 - Prob. 8E Ch. 13.3 - Prob. 9E Ch. 13.3 - Prob. 10E Ch. 13.3 - Prob. 11E Ch. 13.3 - Prob. 12E Ch. 13.3 - Equation of a Tangent Line Find an equation of the...Ch. 13.3 - Prob. 14E Ch. 13.3 - Prob. 15E Ch. 13.3 - Prob. 16E Ch. 13.3 - Prob. 17E Ch. 13.3 - Prob. 18E Ch. 13.3 - Prob. 19E Ch. 13.3 - Prob. 20E Ch. 13.3 - Prob. 21E Ch. 13.3 - Prob. 22E Ch. 13.3 - Prob. 23E Ch. 13.3 - Prob. 24E Ch. 13.3 - Prob. 25E Ch. 13.3 - Prob. 26E Ch. 13.3 - Prob. 27E Ch. 13.3 - Prob. 28E Ch. 13.3 - Prob. 29E Ch. 13.3 - Prob. 30E Ch. 13.3 - Prob. 31E Ch. 13.3 - Tangent Lines (a) If g(x) = 1/(2x 1), find g(a)....Ch. 13.3 - Prob. 33E Ch. 13.3 - Prob. 34E Ch. 13.3 - Prob. 35E Ch. 13.3 - Prob. 36E Ch. 13.3 - Velocity of a Ball If a ball is thrown straight up...Ch. 13.3 - Velocity on the Moon If an arrow is shot upward on...Ch. 13.3 - Prob. 39E Ch. 13.3 - Inflating a Balloon A spherical balloon is being...Ch. 13.3 - Temperature Change A roast turkey is taken from an...Ch. 13.3 - Heart Rate A cardiac monitor is used to measure...Ch. 13.3 - Prob. 43E Ch. 13.3 - World Population Growth The table gives...Ch. 13.3 - Prob. 45E Ch. 13.3 - Prob. 46E Ch. 13.4 - Let f be a function defined on some interval (a,...Ch. 13.4 - Prob. 2E Ch. 13.4 - Limits from a Graph (a) Use the graph of f to find...Ch. 13.4 - Prob. 4E Ch. 13.4 - Prob. 5E Ch. 13.4 - Prob. 6E Ch. 13.4 - Prob. 7E Ch. 13.4 - Prob. 8E Ch. 13.4 - Prob. 9E Ch. 13.4 - Prob. 10E Ch. 13.4 - Prob. 11E Ch. 13.4 - Prob. 12E Ch. 13.4 - Prob. 13E Ch. 13.4 - Prob. 14E Ch. 13.4 - Prob. 15E Ch. 13.4 - Prob. 16E Ch. 13.4 - Limits at Infinity Find the limit. 17. limxcosx Ch. 13.4 - Prob. 18E Ch. 13.4 - Prob. 19E Ch. 13.4 - Prob. 20E Ch. 13.4 - Estimating Limits Numerically and Graphically Use...Ch. 13.4 - Prob. 22E Ch. 13.4 - Prob. 23E Ch. 13.4 - Prob. 24E Ch. 13.4 - Prob. 25E Ch. 13.4 - Prob. 26E Ch. 13.4 - Prob. 27E Ch. 13.4 - Prob. 28E Ch. 13.4 - Prob. 29E Ch. 13.4 - Prob. 30E Ch. 13.4 - Prob. 31E Ch. 13.4 - Prob. 32E Ch. 13.4 - Prob. 33E Ch. 13.4 - Prob. 34E Ch. 13.4 - Prob. 35E Ch. 13.4 - Prob. 36E Ch. 13.4 - Prob. 37E Ch. 13.4 - Prob. 38E Ch. 13.4 - Salt Concentration (a) A tank contains 5000 L of...Ch. 13.4 - Velocity of a Raindrop The downward velocity of a...Ch. 13.4 - DISCUSS: The Limit of a Recursive Sequence (a) A...Ch. 13.5 - The graph of a function f is shown below. 1. To...Ch. 13.5 - Prob. 2E Ch. 13.5 - Estimating an Area Using Rectangles (a) By reading...Ch. 13.5 - Prob. 4E Ch. 13.5 - Prob. 5E Ch. 13.5 - Prob. 6E Ch. 13.5 - Prob. 7E Ch. 13.5 - Prob. 8E Ch. 13.5 - Prob. 9E Ch. 13.5 - Estimating Areas Using Rectangles In these...Ch. 13.5 - Prob. 11E Ch. 13.5 - Prob. 12E Ch. 13.5 - Prob. 13E Ch. 13.5 - Prob. 14E Ch. 13.5 - Prob. 15E Ch. 13.5 - Prob. 16E Ch. 13.5 - Prob. 17E Ch. 13.5 - Prob. 18E Ch. 13.5 - Prob. 19E Ch. 13.5 - Prob. 20E Ch. 13.5 - Prob. 21E Ch. 13.5 - Prob. 22E Ch. 13 - (a) Explain what is meant by limxa f(x) = L. (b)...Ch. 13 - To evaluate the limit of a function, we often need...Ch. 13 - (a) Explain what it means to...Ch. 13 - (a) Define the derivative f(a) of a function f at...Ch. 13 - (a) Give two different interpretations of the...Ch. 13 - (a) Explain what is meant by limx f(x) = L. Draw...Ch. 13 - (a) If a1, a2, a3, is a sequence, what is meant...Ch. 13 - (a) Suppose S is the region under the graph of the...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Estimating Limits Numerically and Graphically Use...Ch. 13 - Limits from a Graph The graph of f is shown in the...Ch. 13 - One-Sided Limits Let f(x)={2ifx1x2if1x2x+2ifx2...Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Finding Limits Evaluate the limit, if it exists....Ch. 13 - Prob. 13RE Ch. 13 - Prob. 14RE Ch. 13 - Prob. 15RE Ch. 13 - Prob. 16RE Ch. 13 - Prob. 17RE Ch. 13 - Prob. 18RE Ch. 13 - Prob. 19RE Ch. 13 - Prob. 20RE Ch. 13 - Prob. 21RE Ch. 13 - Derivative of a Function Find the derivative of...Ch. 13 - Prob. 23RE Ch. 13 - Prob. 24RE Ch. 13 - Prob. 25RE Ch. 13 - Prob. 26RE Ch. 13 - Prob. 27RE Ch. 13 - Prob. 28RE Ch. 13 - Prob. 29RE Ch. 13 - Prob. 30RE Ch. 13 - Prob. 31RE Ch. 13 - Prob. 32RE Ch. 13 - Prob. 33RE Ch. 13 - Prob. 34RE Ch. 13 - Prob. 35RE Ch. 13 - Prob. 36RE Ch. 13 - Prob. 37RE Ch. 13 - Prob. 38RE Ch. 13 - Prob. 39RE Ch. 13 - Prob. 40RE Ch. 13 - Prob. 41RE Ch. 13 - Prob. 42RE Ch. 13 - Prob. 43RE Ch. 13 - Prob. 44RE Ch. 13 - Prob. 45RE Ch. 13 - Prob. 46RE Ch. 13 - Prob. 47RE Ch. 13 - Prob. 48RE Ch. 13 - Prob. 1T Ch. 13 - For the piecewise-defined function f whose graph...Ch. 13 - Prob. 3T Ch. 13 - Prob. 4T Ch. 13 - Prob. 5T Ch. 13 - Prob. 6T Ch. 13 - Prob. 7T Ch. 13 - Work Done by a Winch A motorized winch is being...Ch. 13 - Prob. 2P Ch. 13 - Prob. 3P Ch. 13 - Prob. 4P Ch. 13 - Prob. 5P

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The limit of the sequence a n = n n 2 + 4 .

Solution Summary: The author calculates the limit of the sequence by dividing the numerator and denominator of rational function by the highest power of n.